番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-12/

1. On $m$-fullness in number fields
2. Properness of the Cuspidal Hilbert Eigenvariety
3. A cyclotomic gluing construction for lattice sphere packings
4. Hankel Matrix Decompositions and Digital Sequences over Function Fields
5. Polynomial parametrization of $\text{SL}_2$ over global function field rings
6. A Rigid Analytic Curve Can Have a Dense $p$-adic Orbit
7. A conditional bound $\Lambda\le0.13963$ for the de Bruijn--Newman constant
8. Reciprocal LCM powers and Robin's criterion
9. Reasonable bounds for Restricted Polynomial Progressions in $\mathbb F^n_p$
10. On the Imaginary Part of $\zeta'/\zeta$
11. Odd order cases of Chowla's averages over arbitrary rectangles
12. Product and Quotient Set Dominance in Finite Groups
13. On Quadric Surfaces Weighted by Arbitrary Coefficients
14. Hecke Eigenform Product Identities for Full-Level Hilbert Modular Forms
15. The order types of the supports of $p$-adic algebraic Hahn series
16. Stieltjes constants for Hurwitz-type L-series attached to periodic arithmetic functions
17. Towards linear growth for biprojective hypersurfaces of small dimension
18. Real Fiducial Vectors Only Exist in Dimensions $d\equiv 3 \pmod{4}$
19. On the Quantitative Bounds of Nonlinear Roth Theorem
20. Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$
21. Short Recurrences and Straight-Line Programs for Primes
22. Sharp Bounds for Limits of $N$-Point Correlation
23. Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
24. Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of $(-1)^{\omega(n)}$
25. On a conjecture on Romanoff type representations
26. On Divisor Function Polynomials and Dirichlet Series
27. On the saturability of $p$-adic Lie groups
28. An Infinite Family of Ap\'ery-like Recurrences for Euler's Constant
29. Covering plane curves over finite fields with lines
30. Khintchine dichotomy for images of self-similar measures and almost random walks
31. Higher mod $p$ Satake transforms: explicit formulas and images for $\mathrm{GL}_2$
32. Thurston's Legacy at the Interface of Surface Dynamics, Train Tracks, and Arithmetic
33. Campana strong approximation on generalised Markoff surfaces
34. Weighted, GIT and N\'eron--Tate heights on genus-two moduli and Jacobians
35. Counting with Hiccup Sequences
36. The Tate Conjecture for Ordinary Calabi-Yau Threefolds

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-09/

1. The Integer Values of $\sum_{i=1}^{n}\frac{1}{\gcd(n,i)}$
2. The structure of irreducible cuspidal eta quotients
3. Logarithmic moments of the Rogers Ramanujan continued fraction and odd zeta values
4. Multiplicity Constants for Rough Numbers in Prime Gaps
5. Finite-radius Jensen and relative-entropy formulations of the Balazard--Saias--Yor criterion
6. Simple and accurate approximations to Dirichlet $L$-functions
7. A Generalization of the Riemann Functional Equation with Three Variables
8. Irreducibility of Generalised Laguerre Polynomials for Large Integer Parameters
9. Classification of the Orbits of Three Quadratic Collatz-type Maps
10. Simultaneous non-vanishing of twists of $\mathrm{GL}_3$ and $\mathrm{GL}_1$ $L$-functions
11. Long intervals of consecutive composite values of polynomials
12. Cardinalities of Jordan Diophantine sets of upper triangular integer matrices
13. Non-degeneracy and Fibering with Applications to Diophantine Approximation
14. Equidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^2$ discrepancy
15. Splitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fields
16. Additive Sums of Generalized Shifted Ternary Divisor Functions
17. A note on Riemann's $R$-function and almost primes
18. A combinatorial proof of the quadratic Gauss sum
19. Horizontal moments of Kloosterman sums and a density version of sieves
20. Automorphic symbols and automorphic \emph{L}-values of GL(2) over imaginary quadratic fields
21. Statistics of divisor functions over function fields
22. Ray class monoids for orders of number fields
23. Weak and genuine A_n-formality for number fields
24. Invariant Measures on Smooth Algebraic Groups over Higher Local Fields
25. Discorrelation of the M\"obius function with linear phases in short intervals
26. New Hoffman-type generators for alternating multiple zeta values
27. A Unified Framework for $p$-adic Congruences and $p$-adic Interpolations of Sequences
28. $q$-Supercongruences Modulo the Third and Fifth Powers of a Cyclotomic Polynomial
29. $q$-Analogues of some supercongruences related to Van Hamme's (E.2) and (F.2) supercongruences
30. Uniform Height Gaps in Arbitrary Characteristics
31. Pythagorean pairs in boxes of prime powers
32. Uniform non-vanishing of prime quadratic twists of standard and symmetric square $L$-functions
33. Unipotent Selmer dimensions for CM curves via Iwasawa loci
34. Further bounds in the polynomial Szemer\'edi theorem
35. Hyperplane winning for bad in manifolds
36. A uniform bound for the minimal degree of an isogeny between principally polarized superspecial abelian surfaces
37. Geometric families of multiple elliptic Gamma functions and arithmetic applications, III
38. On $a^4+b^4+c^4+d^4=(a+27(b+c+d))^4$ and ten other new infinite families
39. On Igusa's conjectures for weighted homogeneous polynomials with isolated singularities
40. Slightly improved zero-free half-planes for the quasi-Riemann hypothesis
41. Two Primes and Five Mixed Fibonacci-Lucas Summands
42. Geometrically Abelian Sections on Higher-Dimensional Varieties
43. The Erd\H{o}s-Falconer distance problem in the integer lattice
44. K-Moduli Wall Crossing and Automorphic Forms for the Moduli Space of Rational Elliptic Surfaces
45. K-moduli wall crossing for quasimaps to a projective variety
46. Continuity of the Julia sets in non-archimedean and hybrid settings
47. On the asymptotic behavior of the number variance of random points on the unit torus
48. Arithmetic Progressions in Midpoint Colourings
49. Largeness of the wild locus
50. Rational curves on toroidal compactifications of Picard modular varieties
51. A Complete Proof of Mueller--Ho Conjecture
52. Twisted Jacquet modules and induction from Speh representations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-08/

1. Mean Estimates for Short Polynomial Exponential Sums over Primes
2. Consecutive Cycle Sums
3. More than 83.9% of the zeros of the Riemann zeta function are distinct and more than 67.35% are simple and on the critical line
4. Automorphisms of general modular curves
5. Affine Coordinate Subspaces and Strong Khintchine Convergence
6. Idempotence in Carmichael and Giuga numbers and its application to the Agoh-Giuga conjecture
7. On a Digital Signature Based on Matrix Decomposition and the MinRank Problem
8. On the algebraic and analytic ranks of the twin-prime elliptic curve $y^2=x(x-2)(x-p)$
9. Regular integral models of Shimura varieties and a conjecture of Pappas
10. Higher order uniformity of the primes and cancellation of the M\"obius function in shorter intervals
11. Prime points on smooth hypersurfaces
12. Linear independence of values of polylogarithms with periodic coefficients, outside the disk of convergence
13. Maximal volume of convex bodies avoiding random points and lacunary dilates
14. Translation-invariant equations in $\mathbb{F}_p^n$ and groups
15. Terminal Blocks of Primes in Pisot Numeration Systems
16. Spacing statistics for a point scatterer on the cubic three-torus
17. Consecutive Rankin-Cohen Bases, Full-Spark Periods, and Divisor-Tau Congruences
18. Invariant Primes in Lubin-Tate Space and Hovey-Strickland at Every Height
19. Generating sets for maximal orders in rational quaternion algebras
20. Improved average and almost-all bounds for $G(n)$
21. Irrationality exponents of logarithms of positive rational numbers
22. Intersecting a curve in an abelian variety with multiples of another curve
23. Local Factors in the BSD Conjecture: A Unified Statistical View
24. Cocycle Relations and Elliptic Gamma Values
25. Mixed moments of arithmetic functions and Kloosterman sums
26. $p$-class groups in the cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fields
27. Equivariant Unirationality of Cubic Threefolds
28. Making Every Number from 1 to N Under a Fixed Cycle of $+$, $\times$, $-$, $\div$
29. Points and their multiples on curves in powers of simple abelian varieties

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-07/

1. Densities of Picard Rank Jumps for K3 Surfaces Over Global Fields
2. CUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155
3. On the class number of real multiquadratic fields
4. The One-Power Erd\H{o}s Conjecture for Primes $p \equiv 7 \pmod{36}$
5. Systems of equations with elements of finitely generated groups and with linear recurrence sequences
6. On eutactic forms
7. Lifting ethereal Bianchi modular forms
8. Gaps theorems for linear forms with cubic coefficients
9. Further results on the paramodular Hecke algebra
10. Primitive normal progressions in finite fields
11. A new bound for the Furstenberg--S\'ark\"ozy theorem using the van der Corput property
12. Carlet's cyclic-additive conjecture for the Kasami monomials
13. A concise proof of the 8 case of Sylvester's conjecture
14. The Artin-Davenport conjecture on cubic forms
15. The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer
16. Perfect powers with few digits and $S$-unit coefficients
17. Primitive Fourier Coefficients of Hermitian Klingen-Eisenstein Series
18. Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case
19. Generating and generalizing MSTD sets through Markov processes
20. On S\'{a}rk\"{o}zy's Local Extrema Conjectures
21. The least prime with a given primitive root and a variant of the larger sieve
22. Local newforms, Pa\v{s}k\={u}nas-Stevens Whittaker functions, and explicit test vectors for $\mathrm{GL}(n)\times \mathrm{GL}(n)$
23. New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations
24. New algebraic points on covers of elliptic curves
25. Mixing of the BCZ Map
26. Higher additive energies on discrete cubes
27. Block decompositions in the p-adic Langlands correspondence
28. Semisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varieties
29. Special Loci in the Moduli of Curves
30. On the structure of certain valued fields II
31. Random Cayley sum hypergraphs and $k$-fold sumsets

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-06/

1. The Riemann-Siegel remainder as a fractional summand
2. Gaps, isolated points, and the origin of the ray in the one-dimensional Dirichlet spectrum
3. Exponential generating functions for Apostol-Dedekind and related sums
4. Nonvanishing of special $L$-values of cusp forms on $\mathrm{GL}(2)$ with totally split prime power twists: without the class number hypothesis
5. On Mahler $U$-numbers under rational maps
6. Optimal large sieve for fixed order characters
7. Moments and Large Geometric Monodromy for Linearly Constrained Kloosterman Families
8. Sequential exponential-motivic periods in spatially cut-off $\phi^4_2$
9. Iterated cotangent-difference integrals over totally real cyclotomic fields
10. Prescribed ideal classes and elliptic points in Ennola cubic fields
11. Cubic Progressions on Smooth Plane Curves
12. Note on fractional sum of the divisor function
13. Few small primes suffice to cover unit groups
14. Borwein-Bradley-type identities for Ramanujan-type series for $1/\pi^4$
15. Supercongruences for Domb numbers
16. Proofs of some OEIS conjectures on Wythoff sums, Fibonacci and Lucas words
17. Through the lens of the Eisenstein ideal
18. Error Term Estimates for Sets of Remainders
19. Dyadic Structure of the Two-Block Odd Partition Function and Theta-Weighted Congruences for $pod(n)$
20. An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras
21. On the generalized Sierpi\'nski and Riesel numbers
22. One-level density of zeros of the Riemann zeta function weighted by its special values
23. The main conjecture for a Vinogradov subsystem
24. Sharp mean value estimates in the absence of translation-dilation invariance
25. Four-square polynomial triples: quadratic classification and equal-degree obstructions
26. On the factorization of $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}} + x^{d_{1}} + p$ and a conjecture of C. Nicol
27. Ab-faithfulness of absolute Galois groups in number theory
28. Slope Stability for ${\mathbf Z}_p$-Towers of Curves
29. Amicable numbers
30. An Algebraic Proof of the Non-Modularity of Solutions to the Canonical Modular Differential Equation
31. Ideal-Smooth Sets and an Explicit Upper Bound for the Real Sum-Product Exponent
32. Automorphic commutator relations in relative geometric Langlands
33. Conflict-avoiding codes and near-primitive roots
34. A proper arithmetic surface with infinite \'etale fundamental group
35. When the BSD Real Period Remembers Elliptic Curves over $\mathbb{Q}$
36. A Variant of the Fractional Gamma-regularized Zeta Kernel
37. Tower of coverings and polylog-size coverings of rational points
38. Theta Series with Half-integral Characteristics
39. A Bogomolov property for moduli spaces of polynomials over abelian extensions
40. How close can rational points get to a manifold?
41. Counting zero-sum subspaces for the multiplicative inverse function
42. Golod--Shafarevich for arithmetic surfaces
43. Chowla Conjecture for the truncated M\"obius function over $\mathbb{F}_q[t]$
44. Degeneracy loci and unlikely intersections in abelian schemes
45. $7$-adic Galois representations of elliptic curves over the rationals via Kummer descent
46. The linear independence of $1$, $\zeta(3)$, and $\zeta(4)$
47. ETM-3D: A One-Parameter Multistable Quadratic Flow with an Explicit Absorbing Set and Intermittent Chaos
48. Infinite log-concavity of the Taylor coefficients of the Riemann xi-function
49. Uniform positivity of the tau invariant
50. Weak approximation for Campana points on projective spaces
51. Tempered Symplectic Distinction For Quaternionic $GL_n(D)$: A Conjecture of PRASAD
52. On three conjectures of Kimberling concerning the array $\lfloor k\varphi^n\rfloor$
53. Polynomials with restricted support and maximal zeros on a finite Cartesian set
54. Generic Hodge and special Hodge--Witt polygons
55. Spreading out perverse sheaves

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-05/

1. Arithmetic growth in partially commutative semigroups of endomorphisms
2. The proportion of polynomials over F_2 with positive orthogonal multiplicity
3. Shimura Reciprocity for Real Quadratic Fields
4. Counterexamples for Rational Points Near Curves
5. The Prime Wavelet Tree: Compressing the Carmichael Numbers
6. Extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus
7. A uniform degree bound for modular rank-two Nahm sums
8. The Wang--Sun Sum over Affine Derangements
9. A new upper bound for the irrationality exponent of $\zeta(2)$
10. some arithmetical aspects of the two dimensional jacobian conjecture
11. Telescopic Structure of Numerical Semigroups Generated by Unsigned Stirling Numbers of the First Kind
12. Cohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary Monodromy
13. Cubic arithmetic-geometric mean and isogenies of Hesse elliptic curves
14. Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census
15. Pellarin's Identity, Carlitz Period, and Anderson Generating Functions over Arbitrary Curves
16. The quality plane of $abc$-triples and the decomposition into gains
17. Gosper's and Ramanujan's infinite products and generalizations
18. A cubic Chabauty criterion for hyperelliptic curves
19. Eisenstein congruences in tame families and the class group of a metabelian extension
20. Sum-product patterns in the shifted primes
21. Hausdorff dimension for exactly approximable matrices
22. Explicit second moments of symplectic Siegel transforms
23. Quantitative Gowers uniformity of the primes in intervals of length $X^{5/8+\varepsilon}$
24. Exact diameter compression for four-point sumset cardinalities
25. Pappas's conjecture on ramified unitary local models
26. Resolving Erd\H{o}s-Ulam Monochromatic Union-Closed Family Conjectures
27. Sharp rational points counting near nondegenerate curves in $\mathbb{R}^n$
28. Sturmian beta-shifts do not have typical periodic optimization

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-02/

1. Two-Line Elimination and the Weierstrass Group Law in Arbitrary Characteristic
2. PageRank on Lubotzky--Phillips--Sarnak graphs
3. Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)
4. An explicit family of twists of the Carlitz module with unbounded analytic rank
5. New bounds for the integer Chebyshev constant of [0,1]
6. On a problem on Ramanujan-Sato series of level 11
7. Perfect squares in reciprocal-sum sequences and primes that are inert in quadratic fields
8. Congruence Jumping in Polynomial Divisibility Systems: Arithmetic Structure and Solution Sets
9. Multiplicative recurrence of Piatetski--Shapiro and nil-Bohr sets
10. Transcendence of dendric beta-expansions with pure discrete spectrum
11. Powers in orbits and semigroups generated by polynomials
12. Construction of parametrized families of general pseudo-bimagic and bimagic squares
13. Baire-category transfer between Engel and Pierce expansions
14. Indefinite theta vectors and generalized Nahm sums of arbitrary rank
15. The sixth moment of the Riemann zeta function
16. Translation invariant quadratic forms in $8$ variables and dense sets of primes
17. Sharp $p$-adic Extrema and Least Extremal Rows for Restricted Binomial GCDs
18. A Prime-Power Dichotomy for Nekrasov--Okounkov Hook Lengths and $t$-Core Partitions
19. Tridimensional character sums with polynomial arguments and applications
20. Uniform estimate of Lang-Weil type for counting points of schemes over finite rings
21. Quadratic distances in even dimensions over prime fields
22. Averages of Artin characters and their relation to the Davenport--Heilbronn theorem
23. Square products of factorials and a conjecture of Erd\H{o}s and Graham
24. Supersingularity and Superspeciality Verification of Abelian Surfaces
25. Infinite free pro-p products as absolute Galois groups
26. On the prime geodesic theorem
27. On The Index of Polynomial Compositions over Valued Fields
28. Direct Group Laws on Classical Genus-One Models
29. Markov chains arising in the study of random matrices over pro-finite rings
30. Transcending Algebraic Geometry
31. Mock Modularity, Resurgence, and Dual False Theta Functions
32. A Combinatorial Approach to the CUE Joint Moment Problem
33. Intersecting integer partitions: star bounds and counterexamples at every scale
34. Recurrent two-dimensional sequences over three and four letters simulating von Neumann constructions of finite ordinals
35. Complex hyperbolic surfaces whose closed geodesics are all simple

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-01/

1. A Romanoff-type theorem for a multiset of products of powers
2. Strong Artin Conjecture for Generalized Octahedral Representations in $\mathrm{GL}_3$
3. Large gaps between Romanoff numbers
4. Euclidean Triangles Associated with Diophantine $D(4)$-triples
5. Zeta elements for $p$-ordinary modular forms over imaginary quadratic fields and applications
6. Monogenity of the irreducible factors of $(k,t)$-Fibonacci and $(k,t)$-Lucas polynomials
7. On a problem of Nathanson related to strongly minimal asymptotic bases of order $h$
8. The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithms
9. The cardinality of a set containing the pairwise sums of four positive integers
10. Limit distribution of algebraic integral points on curves
11. Finite-slope p-adic L-functions for $\mathrm{GL}_{3}$
12. On the Quotient of a Pseudo-null Module
13. Asymptotic and Arithmetic Aspects of Generalized Colored Overpartitions
14. The sixth moment of a degree two $L$-function of arbitrary level
15. Atkin--Lehner Quotients of Modular Curves at Primes of Bad Reduction
16. Sharp spherical extension theorem in $\mathbb F_q^{2m}$ and applications
17. On a question of Jones on tracelike vectors, cusp forms, and von Neumann algebras
18. Rational quadrilaterals and tetrahedra -- the involutions of Kummer, Heegner and Regge
19. Galois groups of random polynomials of large degree
20. Semi-stable models, local heights and quadratic Chabauty for $X_0(N)^*$
21. A proof of Hirose's duality conjecture
22. Resurgent rigidity of mock theta functions: uniqueness and natural boundary crossing
23. On Greenberg's conjecture for rational elliptic curves at Eisenstein primes
24. On c-polynomial factorisations
25. The Bias Conjecture for One-Parameter, Non-Isotrivial Elliptic Curve Families
26. On the coefficients of the asymptotic of analytic torsion
27. Canonical representatives and interval independence in Ekedahl's equivalence
28. Diameter and radius of an additive-multiplicative graph
29. On Irreducibility and Multiplicity One Property for Non-Archimedean Type-II Theta Lifting

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-30/

1. Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotients
2. Primes in arithmetic progressions and Siegel zeroes
3. p-adic Rigidity and Supercongruences at Rank Two Attractors
4. Strongly Pseudoperfect Numbers
5. A $q$-analogue of a binomial supercongruence
6. On closed-form expressions for weighted mean square of the Riemann zeta function and Dirichlet $L-$functions
7. On Vojta's harder implication, height inequalities for admissible pairs, points of bounded degree and Deligne-Mumford stacks
8. Twisted Diophantine Approximation I: Asymptotic Theory
9. Twisted Diophantine Approximation II: Uniform Theory
10. Reduction of Weil-Deligne Representations
11. Farey Symbols for the Picard Group
12. A Local Approach to Monogenity with an Application to Lenny Jones' Conjecture
13. The Index of Composition of polynomials and its applications
14. Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements
15. On Boston's Unramified Conjecture for $\GL_2$ and McLeman's $(3,3)$-Conjecture
16. The Algebra of Parity-Twisted Crank Moments and a Prime-Detecting Expression
17. Truncated pretentious distances of multiplicative arithmetic functions
18. On an infinite family of cubic fields with explicit fundamental units
19. Products of two elements of Granville's random model in residue classes
20. Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture
21. A closed-form law for the Salikhov-Zeilberger-Zudilin-Bai family, and computational evidence that Bai's point is optimal
22. Weighted equidistribution of factorial prime valuations in fixed power bands
23. An infinite family of counterexamples to Goss's conjecture on L-functions of cyclotomic function fields
24. A negative answer to Erd\H{o}s Problem #786
25. Uniform Estimates for Integers with a Large Smooth Part
26. A Short Proof of a Theorem of Pan and Zhang
27. Ax-Schanuel for the Drinfeld $j$-function
28. On minima of theta and Epstein zeta functions in dimension four
29. Criterion set for diagonal forms of higher degree
30. Restricted Binomial GCDs at Primes Congruent to -1
31. Smyth's Conjecture on the Mahler Measure of non-reciprocal trinomials of height $1$
32. Congruences for the Andrews--Uncu partition function $\mathcal{EO}_u(n)$
33. Computing residual representations of abelian threefolds with imaginary multiplication
34. Improved exponent bounds for Erd\H{o}s--Selfridge curves
35. Sharp Thresholds for Distance Patterns in Random Subsets of $\mathbb Z^d$
36. Resultants, Recursive Formulas and Binet Formulas for $\textrm{SU}(N)$ Verlinde Sums
37. Square matrices with integer eigenvalues under entry permutations
38. A Memory-Magic Exchange Law in Streaming Clifford+T Compilation
39. Mordell--Lang plus Geometric Bogomolov

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-29/

1. Tamagawa numbers and torsion of elliptic curves over function fields
2. Efficient Computation and Congruences for Colored Partition Functions
3. Quasimodular Forms, Partitions, and Primes in Intervals
4. Conductors and Quadratic base change
5. Factorizations in algebraic monogenic semidomains
6. Unit fractions with semiprime denominators: an elementary proof of Erd\H{o}s Problem #306
7. On the sum of odd minimal excludants over overpartitions
8. Matrix Solutions to the Diophantine equation $X^4+ Y^4=2Z^4$
9. On the Ordering and Injectivity of Lagrange Constants Associated with Certain Substitutions
10. On Fermat-type equations of signature $(r,r,p)$
11. Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the Parts
12. Lower Bounds for Moments of Automorphic L-functions
13. The infinite sum of the cubes of reciprocal balancing numbers
14. Pseudo-Effectivity in the Skolem-Mahler-Lech Theorem
15. Skew cyclic codes through Drinfeld modules
16. Adelic reduction of module lattices
17. A Unified Approach to Formal Arakawa-Kaneko Type Zeta Values via Iterated Integrals
18. Escape and Non-Escape of Mass for Monogenic Binary Cubic Forms
19. More than 83.69% of the zeros of the Riemann zeta function are distinct
20. Dynamics of multiples of zeta by exponential functions
21. Stacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite Fields
22. The Beilinson--Bloch heights of generalized Ceresa cycles
23. Prime-Detecting Identities from Dirichlet Inversion
24. On the distribution of the zeros of the Euler double zeta-function $\zeta_2(s,s)$
25. A Padovan-automatic description of a nested recurrence
26. An elementary treatment of Ramanujan's elementary continued fractions
27. Cancellation profiles of Fibonacci-Lucas zeta sums
28. $k$-Fibonacci and $k$-Lucas numbers with the H\"older inequality
29. Biases in the distribution of primes in short intervals
30. Cyclotomic factors and irreducibility of the denominators of $q$-deformed rational numbers
31. Necessary and sufficient condition for reciprocal polynomials to be monogenic
32. The two-block odd partition function
33. Rank stability of elliptic curves over $\mathbb{F}_q(t)$ in residue classes
34. Higher-order colossally abundant numbers
35. Omega bound for the Piltz divisor problem
36. Square root cancellation in the hyperbolic lattice counting problem over cocompact groups
37. An improved high-low method for the parabola
38. Sums of von Mangoldt convolutions via trace-sum averages over $U(N)$
39. Coxeter Symmetry in Hypergeometric Functions and Elliptic Integral Moments
40. Density of $\mu$-ordinary Primes for K3 Surfaces
41. Exceptional poles of archimedean Asai $L$-functions
42. Plectic Lie Algebra Action on Hilbert modular varieties
43. Structure of derived Hecke algebras with coefficients in torsion-free profinite rings
44. A new proof of two-color partition regularity of Pythagorean triples
45. Hausdorff Dimension of Weighted Singular Vectors
46. Moments of random multiplicative functions with polynomial coefficients
47. Weak Hall's conjecture, approximation gains, and continued fractions
48. Singular intersections in split semiabelian varieties
49. On a generating function of the basis of weakly holomorphic functions on an elliptic curve
50. Complete classification of $7$-adic Galois images for non-CM elliptic curves over $\Q$
51. A note on large clusters of $E_2$-numbers
52. On the largest prime factors of $p-1$ and $p+1$
53. A difference formula of $p$-adic height pairings via the Bloch-Kato logarithm map
54. Heavenly Elliptic Curves over Cubic Number Fields
55. The modal expansion of Kempner sums
56. Sharp lower bounds for the periodic maximal Schr\"odinger operator in higher dimensions
57. Very sparse return sets in arithmetic dynamics
58. A planar algebraic Zarankiewicz theorem over prime fields
59. Generic Points on the Staircase and Irregularities in Uniform Distribution
60. Uniform Unicellular Dessins d'Enfants with Trivial Automorphism Groups
61. $p$-adic spectral zeta functions via the inverse Stieltjes transform
62. A quasipolynomial inverse theorem for the $\mathsf{U}^k(\mathbb{F}_p^n)$ norm in the high characteristic
63. Perfectoidness of Proper Shimura Varieties With Limpid Integral Models
64. Gauss--Manin connections extend to holonomic coadmissible D-cap-modules
65. Some applications of binary numeration systems with nonzero redundancy to the theory of locally complex functions
66. Automorphic $C^*$-algebras of reductive groups
67. A uniform lower bound for the Zhang-Kawazumi invariant and applications to the Bogomolov conjecture

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-28/

1. A Congruence Conjecture of Z.-W. Sun for Reciprocal Central Binomial Sums
2. Supercharacter theory and applications to Ramanujan sums over a finite Frobenius ring
3. On the Langlands--Kottwitz--Scholze method
4. Congruence obstructions in the refined Koblitz conjecture
5. Local Weak Maass Forms and Traces of Cycle Integrals
6. Pinch's conjecture on $a$-convexity
7. Mishiba's Conjecture on the Coaction of $\infty$-adic Multiple Zeta Values
8. Counterexamples to the inhomogeneous Duffin-Schaeffer conjecture for a residual set of shifts
9. Upper and lower fluctuations in Shallit's law of leap years in Pierce expansions
10. Counterexamples to the inhomogeneous Duffin-Schaeffer Conjecture
11. On the Moments of Least $r$-Gaps of Partitions and a Conjecture of Baruah and Talukdar
12. The derivative function of the zeta-star correspondence
13. Experiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion point
14. A parametric Catalan-type congruence for generalized central trinomial coefficients
15. Irreducible rootless unimodular lattices generated by vectors of norm $3$
16. Ternary Perfect Forms Over Imaginary Quadratic Field
17. Further Results on Sum-Freedom of Binary and $q$-ary Functions
18. On Conjectures of $\mu$-Invariant for Selmer Groups at $p=2$
19. Computing the Iwasawa $\mu$-Invariants for Elliptic Curves over $\mathbb{Z}_2$-Extensions
20. On the infinite sum of reciprocals of the fourth powers of balancing numbers
21. Free semigroups of power series
22. Galois groups of integer polynomials with prescribed coefficients
23. Formal groups and $(\varphi,\Gamma)$-modules
24. Galois groups of twisted reciprocal polynomials: a uniform asymptotic
25. The geometry of solutions to the general sextic
26. Cartier--Dieudonn\'e Theory of Connected Group Schemes
27. Comment on "Symmetric Pseudo-Random Matrices"
28. A Mathematical Theory of Near-Field Super-Resolution

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-25/

1. Rank-two Nahm sums, modularity obstructions, and the McKay--Thompson series $T_{31A}$
2. Noncongruence cusp forms, Veech groups and enumeration
3. Effective logarithmic two-point Chowla bounds in every window
4. Permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fields
5. Straight-line programs for the solutions of Pell's equation
6. Computations of Cohomology of Arithmetic Groups, Part 1
7. On the index of generalized trinomials over Valued fields
8. Computing the cohomology of Shimura curves in quasi-linear time
9. Congruence Classes of Supporting the Erd\"{o}s-Straus Conjecture II: Wild Solutions
10. A new lower bound for the Schur-Siegel-Smyth trace problem
11. Refinements of Peck's theorem on simultaneous approximation to algebraic numbers
12. Counting consecutive multiplicatively dependent triples
13. A geometric proof of Peck's theorem
14. A power-sum obstruction to cyclotomicity in a family of symmetric numerical semigroups
15. Lie algebras for multiple Eisenstein series and multiple q-zeta values
16. The Fermat-Type Matrix Equation over $\mathrm{GL}_2(\mathbb{Z})$
17. Reducibility of $rx^m+p^e f(x)$ for Large Primes $p$
18. On murmurations
19. Arithmetic progressions in dense subsets of primitive elements of finite fields
20. Self-intersection Points of Billiard Trajectories in a Square with Small Pockets
21. On the density of $A+B$ when $B$ has few elements
22. On smooth elements in arithmetic semigroups
23. Infinitely Many Off-Critical-Line Zeros of the Tempered Xi Function: A Disproof of Yang's Conjecture
24. Identities and congruences involving orthogonal polynomials and Ap\'ery-like numbers
25. A note on isomorphism types of complete discretely valued fields of mixed characteristic
26. Computing the divisor summatory function in $N^{9/28+o(1)}$
27. Sparsity of rational points on torsion level covers of Hilbert modular varieties
28. Diophantine approximation by primes and Landau--Siegel zeros
29. Lonely Runner Relations
30. The Schur multiplier of $\rm{SL}_2$, $K_2$, and Dedekind zeta-functions over $S$-integers
31. Pro-$\mathbf H_p$ density in the free group of rank two: a Frobenian criterion on the mod-$p$ torus
32. Proof of the positive trace gap conjecture
33. On the DML(1) property for regular endomorphisms of affine spaces: the $\mathbb{G}_m$-case
34. Congruence Classes in $\mathbb{F}_p^2$: Sharp Results via an Energy Approach
35. Disproof of a Conjectured Upper Bound for the Davenport Constant
36. Total rings of quotients of higher dimensional Iwasawa algebras
37. A computable wandering and tracelike vector for modular orbits in the Bergman space
38. High Rank and Multiplicity in Random and Perfect Profinite Groups
39. Frobenius lifts and point counting for smooth curves

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-24/

1. A new upper bound for the irrationality exponent of zeta(3)
2. The Primitive Generalized Fermat Equation x^3+y^5=z^7: A computer-assisted proof
3. Galois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas
4. $A_2$-frames, negacyclic glue, and extremal strongly $6$-modular lattices
5. The number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety
6. Definability and undecidability via the torsion subgroup of units
7. Completed cohomology of Hilbert modular varieties below middle degree
8. Geometric lifting and Freiman's $3k-4$ theorem in compact connected abelian groups
9. A proof of the Baruah--Gogoi conjecture on sums of odd and even overlined parts
10. Infinite families of pairs of real quadratic fields whose class numbers are divisible by a given integer
11. Definite integral Albert algebras: arithmetic and finite geometry
12. Modular integrals for individual modular knots
13. Construction of vector-valued adelic automorphic forms
14. Zero density estimates for $\mathrm{GL}_2$ automorphic $L$-functions
15. Gevrey localization for simple and distinct zeros in a prime-modulus Dirichlet family
16. An Approximate Version of Vu's Theorem on Economical Subbases For Non-Integer Exponents
17. Shifted log-sine integrals and multiple zeta values
18. Morse Topology, Zero Products, and Elliptic Prime Crossings
19. On some $D(u^2)$-triples and quadruples of triangular numbers
20. Beyond the unique pair: a two-parameter family of rational triangles with equal perimeter and area
21. The Arithmetic of Reducible Rank 2 Hypergeometric Motives
22. An Introduction to the Lagrange and Markov Spectra through the Lens of Generalized Markov Numbers
23. Weighted bilinear identities and supercongruences for Ap\'ery-like polynomials
24. On the hyperbolic prime number theorem
25. Distinguishing Gauss sums
26. A tyro's approach to the tilted sieve: beyond the Erd\H{o}s--Rankin bound
27. Counting $k$-tuples of positive integers such that the values of several polynomials of $k$ variables are relatively prime
28. Rankin-Cohen Pairings and Hilbert Hecke Eigenform Product Identities
29. On the monomials of Poincar\'e Series of negative index
30. Trivial zeros of zeta functions of type $\mathrm{A}_r$
31. Delta Characters and Filtered Isocrystals
32. On the distribution of the minimal length of addition chains
33. A Szemer\'edi-Trotter Theorem in Arbitrary Fields
34. The intersection of local Arthur packets for even orthogonal groups and applications
35. A minimal HRT counterexample at the sharp Gelfand--Shilov threshold
36. Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$
37. The Tate conjecture for powers of abelian fourfolds and the Hodge conjecture for powers of CM fourfolds
38. Locally analytic representations in mixed characteristic via stacks
39. Endoscopic liftings and parameters of epipelagic representations for classical groups
40. Evaluating $\mathrm {SU}(3)$ Verlinde sums using spectral graph theory
41. Computation of anisotropic singular sums from high-order derivatives of Epstein zeta functions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-23/

1. Infinitely Many Binomial Coefficients of Deficiency One
2. Carmichael numbers of the form $2^n p^m+1$ with odd exponent $m$: refinements of a theorem of Florian Luca, a general independence lemma, and a computational study
3. An Integral Representation of the Generalized Fibonacci Numbers
4. Brauer-Kuroda relations for ramified graph covers
5. The Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell Conjecture
6. Moulds, Bimoulds, and some Lie algebras
7. A density version for the sum of nine cubes of primes
8. On the Euler transform and the floor function
9. Distinct exponents in the prime factorization
10. Irreducible polynomials with restricted digits in base $b(T)$
11. On the generation of multiplicative groups by small primes
12. The density of sums of distinct divisors
13. Density of large holes among power-free lattice points
14. A surprising generalization of the M\"{o}bius function
15. S-integrality for families of ordinary K3 surfaces and algebraicity theorems
16. On the positivity of truncated pentagonal number series and some conjectures of Merca
17. Irrationality Exponents and Partial Quotient Growth in Continued Fractions
18. Abelian $p$-extensions with restricted $p$-ramification and the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q} (\sqrt{q})$
19. The large sieve through Parseval, Large sifted sets are regular
20. The weighted large sieve through Parseval
21. Large values of the Hurwitz zeta function with rational parameter
22. Equal subset sums and close divisors
23. Boyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_k
24. A certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of Samart
25. Peels of Equilateral Triangulated Surfaces
26. On two families of period integrals related to Catalan's constant
27. Improved rational approximations to Catalan's constant
28. Cokernels of random $p$-adic orthogonal matrices and their linearizations
29. Iterated integrals for generalized Appell functions
30. A divisibility of automorphic periods for the real quadratic base change of $\mathrm{GL}_3$
31. Stable base change from unitary groups in three variables and integral relation of automorphic periods
32. Remarks on the Geometry of Sets in $\mathbb{Z}^d$ with Small Fourier $L^1$ Norm
33. The existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubes
34. The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials
35. Extreme values of central $L$-derivatives and heights of Heegner points
36. A finite arithmetic form of Robin's inequality and its equivalence to the Riemann hypothesis
37. An irreducible decomposition of the Weil representation restricted to open compact subgroups
38. The unique extremal threemodular lattice of rank 26, the generalized hexagon $(2,8)$, and the tight Cayley-plane $5$-design
39. Approximating Pi (and other constants) by Radicals in the Footsteps of Rabbi Abraham Ibn Ezra and Guru RSJ Reddy
40. Ergodic Averages over Shrinking Sectors of $\mathbb Z[i]$
41. Continuous Optimization for p-adic Models
42. Zero-Run Spectra of the $(3,2)$ Raney numbers Modulo Primes
43. Eisenstein scattering and Plancherel decomposition on cuspidal Bruhat-Tits quotients
44. Resultant of an equivariant polynomial system with respect to a direct product of $r$ symmetric groups
45. Support-Primitive Decomposition of Constacyclic Codes over Finite Fields: Coefficients-Based and Roots-Based Descriptions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-22/

1. Superpolynomially Large Support in Every Irreducible Factor of Lacunary Polynomials
2. Iwasawa theory of class field towers
3. A quadratic-residue dichotomy for two partition functions modulo 3
4. On periods of the Tribonacci sequence modulo primes
5. Monogenic Fields of Cryptographic Size
6. Bad Reduction of Genus Two Curves with complex multiplication
7. Almost Trivial Units in Group Rings
8. Zero density theorems for short intervals
9. Maximal Unramified $p$-Extensions with Prescribed Galois Groups: A Quantitative Refinement of Ozaki's Theorem
10. On a Tur\'an's theorem for small primes
11. On a Tur\'an's theorem for arithmetic progressions
12. Romanoff type theorems for polynomials over finite fields
13. Steinness of the Basic $\mathrm{GL}_n$ Local Shimura Tower in Odd Rank
14. On $\mathbb{Z}_2$-extensions of real quadratic fields with class group of $2$-rank three
15. Counting number fields with symplectic Galois group
16. The variance of the number of lattice points in narrow sectors
17. Explicit bounds for the prime number theorem
18. Wave Numbers: Discrete Sequence Algebras, Sieve Projectors, and Dynamical Geometry
19. $v$-adic Chowla-Selberg formula over function fields
20. Critical Pairs for Mixed Restricted Sumsets in Prime Fields
21. A two-step supercongruence for an Ap\'ery-like sequence
22. Large values of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian field
23. Lower-order terms in mean-square formulas for the Euler--Zagier double zeta-function and regularized multiple zeta values
24. Higher Reciprocity, Cassels Pairings, and Selmer Towers for the 3/5 Congruent Number Problem
25. Refined sum formulas for finite multiple zeta values of level two
26. Two Legendre-symbol determinants of Sun and Bernoulli numbers
27. Concave transforms and volumes of adelic line bundles
28. Selmer groups of CM-twists of elliptic curves
29. Interpolation determinants and the Lebesgue--Nagell equation $a^2-D=b^p$
30. On the noninjectivity of Jordan's totient functions
31. Detecting split surfaces, RM surfaces, and minimum walks on isogeny graphs
32. Non-Archimedean Poincar\'e series and geodesics on the Bruhat-Tits tree
33. The exceptional set of a prime and a square
34. On existence of generalised Lehmer numbers modulo primes
35. Imaginary Non-CM Fields of $2$-Power Degree
36. A fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modules
37. Proofs of eighteen conjectural identities related to the modulo nine Kanade--Russell identities
38. Sharp zero estimates for trajectories of polynomial vector fields
39. Proportions of the non-trivial zeros of the Riemann zeta function
40. Selberg sieve weights and sign changes of Kloosterman sums. I. Uniform asymptotics for shifted weights
41. Selberg sieve weights and sign changes of Kloosterman sums. II. Square-free moduli with at most four prime factors
42. On the abundance of rigid meromorphic cocycles for quadratic forms in four variables
43. The lower bound of shifted primes with large prime factors
44. $D$-elliptic modular curves $X_0(N)$
45. Asymptotic Behavior of Iterated Sets of Remainders
46. Weighted Generalizations of Zagier's Phenomenon
47. The local Dold congruence for Fibonacci and Lucas sequences
48. On Normality Preserving Operations
49. Geometry around unramified CM points
50. Algebraic independence of periods of Anderson modules and their hyperderivatives
51. Exceptional maps and abelian points in backward orbits
52. A polynomial basis for the multizeta algebra in positive characteristic
53. Abelian dynamical Galois groups over global function fields
54. $\Kab$ has the Bogomolov property for canonical heights
55. The Hall-Janko Simple Group and the Icosian Leech Lattice
56. Extremal Least Common Multiples in Rows of Pascal's Triangle
57. Existence of a Hall ray in higher dimensional Lagrange spectra
58. Sum of Three Squares and Particle in a Cubic Box - Degeneracies
59. Quantum modularity in refined topological recursion
60. Fundamental Lemmas in Universal Resolution
61. From Dimension Drop to Aperiodic Order
62. Density of almost squares of horospherical orbits in non-uniform quotients of $\operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-21/

1. On permutation-invariant construction of glued lattices
2. Extreme value laws for intrinsic Diophantine approximation on spheres
3. Eigenvectors of $p$-Curvature for Geometric Difference Equations
4. Galois deformation rings and modularity in the residually reducible case
5. On The Cyclicity of Algebraic Lattices
6. The large sieve for square moduli under Hooley's hypothesis $R^*$
7. Annular Frobenius Classification of p-adic Stieltjes--Schwarzian Equations
8. The integer group determinants for $\mathbb{Z}_p^n$
9. Difference of the Sum of All Odd and Even Overlined Parts of Overpartitions
10. Frobenius Numbers Associated with Primitive Pythagorean Quadruples
11. Arithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matrices
12. A Note On Certain Minimal Excludants Over Overpartitions
13. On low-discrepancy sequences and Poissonian pair correlation
14. Higher Labute-Serre duality and Lyndon words
15. Non-existence of sets with few special directions
16. Real quadratic fields and finite quantum dilogarithms I
17. $\mathbf{Bad}(\mathbf{r};\mathbf{s})$ is Hyperplane Absolute Winning
18. An equivariant version of Gabber's lemma
19. On the Injectivity of Elementary Symmetric Partitions and the Multiset Recovery Problem

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-18/

1. Asymptotic counting of integers with prime factors $p_{r^a s^b}$
2. Endoscopic description of the local Langlands correspondence for $\mathrm{G}_2$
3. A uniform proof approach for congruences modulo 3 for partitions with $k$-colored odd parts
4. A new family of maximal curves not covered by the Hermitian curve
5. Simultaneous nonvanishing of quadratic twists via Rankin-Cohen brackets
6. Finite subgroups of outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields
7. Norms of Schneider--Teitelbaum Polynomials in $p$-adic Fourier Theory
8. Sampling and Moments of Reciprocal Quadratic Mellin Integrals
9. On a question of Ruzsa about densities of sumsets
10. A characterization of Sophie Germain primes - II
11. The Three Gates: A Rooted-Operator Approach to Weil Positivity
12. A problem of Yang and Chen on weighted representation functions
13. Low moments of automorphic random multiplicative function sums
14. Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
15. Computational results on sums of a prime with squares or cubes
16. Rogers--Ramanujan identities from the geometry of $X^a=Y^b$
17. An ergodic approach to equations of the form $x+y=\lfloor\alpha(n)\rfloor$
18. Sumsets of Ahlfors--David regular sets
19. On the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrm{G_2}$
20. A complete classification of permutation binomials of the form $X^r(X^{q-1}+a)$ over finite fields
21. Infinite prime sumsets in structured and $U^k(\Phi)$-uniform sets
22. Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I
23. Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II
24. Logarithmic--exponential preparation in sharply o-minimal structures
25. Combinatorics of hyperplane arrangements and Witten zeta function at the origin
26. Morphism spaces on low degree hypersurfaces

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-17/

1. Distinct Consecutive Products
2. Transcendence measure for the values of the logarithmic derivative of the Bessel function $J_0$ at algebraic arguments
3. Lattice points close to a smooth curve and squarefull numbers in short intervals. II
4. Effective Hecke eigenvalue equidistribution over the Atkin--Lehner subspaces
5. Only finitely many modular Jacobians are supersingular modulo a given prime
6. On two forms in many variables of different degrees
7. Zero-Density Concentration for Dirichlet Polynomials
8. Unramified Geometric Iwasawa theory of function fields
9. Surjectivity of the Enots Wolley Sequence
10. Continuous approximation to the reciprocal sum of the cubes of Fibonacci numbers
11. Exact universal normalizations for the G\'al--Koksma lemma
12. Nonvanishing of ray class $L$-functions
13. A $q$-recurrence for a finite Ap\'ery limit
14. Graded Algebras of Modular Forms and Sign Changes of Fourier Coefficients for Eta Quotients
15. Bounded intervals containing a given number of primes
16. Extreme Values of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$
17. Cyclotomic Prime Extractors
18. Periodicity conjectures for all 2-sumfree sequences
19. Extreme values of Euler-Kronecker constants of cubic abelian fields
20. Stable Trace Formula for Newton strata of Shimura varieties
21. On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
22. On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients
23. A uniform effective Andr\'e--Oort result
24. An Omega result for partial sums of the Riemann zeta function
25. $\Omega$-results for the logarithmic derivative of $\zeta(s)$ on vertical homogeneous progressions
26. Arithmetic Constraints and Limit Laws for Diagonal Rational Partitions
27. Finite Fourier Duality, Radial Values, and Arithmetic of a Mod Eight False Theta Quotient
28. Transcendence criteria for the minimal word of the rational base $3/2$
29. Tunnell-type criteria for variants of the congruent number problem
30. Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups
31. The non-spherical sup-norm problem for $\mathrm{GL}(n)$ and generalized spherical functions
32. Two proofs of the Cassels--Swinnerton-Dyer conjecture for cubic surfaces
33. Generalized DCCQ: From Binary Quotients to Multinomial Simplex Geometry and Critical-Strip Coordinates
34. On the singularities and the Kodaira dimension of unitary Shimura varieties
35. A somewhat sure note on an un-Schur problem
36. Graph lattice sums and graph zeta functions for long-range interacting quantum lattice models

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-16/

1. The Waring-Goldbach problem in short intervals under the Generalized Riemann Hypothesis
2. Mean Lindel\"of Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds
3. A formula for the rank over $\mathbb{Q}(t)$ of the elliptic curve $y^2=x^3+At^6+Bt^3+C$
4. Number fields as curves over $\mathbf{F}_1$
5. Simultaneously small continued fraction entropy and base $b$ entropy
6. Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences
7. Rational Points near Monofractal Curves and the Strong Oscillation Principle
8. Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
9. Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization
10. Twisted Rational Zeros and Local-Global Principles for Linear Recurrence Sequences
11. Higher Schwarzians of Elliptic Double Covers and Eisenstein--Kronecker Functions
12. The Furstenberg-S\'ark\"ozy theorem for sums of an even number of odd powers
13. An infinite family of imaginary biquadratic fields with a large class number
14. Laurent series expansions for the Barnes multiple zeta function
15. Triple divisor type functions in arithmetic progressions to prime power moduli
16. Iwasawa theory of (directe) Cayley graphs
17. The Local Ghost Theorem in the Tr\`es Ramifi\'e Case
18. Distribution of squarefree integers with double congruence conditions
19. Prime-power congruences for level-one eigenforms
20. Extreme values of quadratic Hecke $L$-functions
21. On $t$-sumfree sequences
22. Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect
23. An additive problem in connection with some quadratic real fields with class number one
24. Powers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd Parts
25. Refined conjectures on Fitting ideals of BDP Selmer groups
26. Modular functoriality for finite groups
27. Uniform Mordell-Lang conjecture for semiabelian varieties
28. A class formula for effective Anderson motives
29. On Sarnak--Str\"{o}mbergsson conjecture
30. Improved bounds for Szpiro's conjecture
31. Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent
32. Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields
33. Loop spaces, twistor $\mathbb P^1$ and tempiric parameters
34. List Decoding, Linear Hashing, and Furstenberg over $\mathbb{F}_q$
35. Block-count constrained harmonic sums: spectral expansion and block-directed Euler-Maclaurin
36. On a classical zero-sum invariant II: Disproof of a long-standing conjecture
37. Small degree isogenies between conjugate principally polarized superspecial abelian surfaces
38. A perimeter analogue of Franklin's identity and an inequality related to the parity of parts

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-15/

1. The Strong 24-Conjecture
2. Theta functions after Weil
3. Dynamical uniform boundedness for unicritical polynomials and elliptic curves of large rank
4. Arithmetic Siegel-Weil for the spherical Hecke algebra
5. Galois representations and modularity for twisted moments of Kloosterman sums
6. Pointwise ergodic theorems along sequences of intermediate growth
7. Spherical statistics and phase transitions in high-dimensional lattices
8. Finiteness of an Isogeny Class via Equidistribution
9. Prime and Nonprime Totatives: A Sharp Construction and Exact Thresholds
10. The optimal scale in Linnik's microsquare problem for almost all integers
11. Generalized Wieferich primes and monogenic polynomials
12. Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups
13. A Local Proof of Langlands's Second Main Lemma for Local Epsilon Factors over Nonarchimedean Local Fields
14. Modular and Shimura curves $X_0^D(N)$ embedded in $\mathbb P^1 \times \mathbb P^1$
15. Reduction of integer tiles via CRT and base-p digits
16. Patterns in the Markov numbers and their generalizations
17. Quantitative linear independence for square roots
18. Twisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan Congruences
19. On Decomposition of Drinfeld cusp forms of level $t$
20. Golden-ratio growth of Conway's subprime closure
21. Two-Height Approximation and Mahler's Problem on Liouville Numbers
22. A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks
23. Surjectivity of Finite Rank-Capped Enots-Wolley Sequences
24. The Jensen--P\'{o}lya program and inequalities for arithmetic sequences
25. Cubic AGM graphs and Hessian $3$-isogenies over finite fields $\mathbb{F}_q$ of odd characteristic with $q \equiv 2 \pmod3$
26. Character sums on an oriented singer conic and explicit Ramanujan double covers
27. An explicit power-saving bound for S\'{a}rk\"{o}zy's Theorem on shifted primes, assuming GRH
28. Bloch cycles and the weak two-variable Chinburg conjecture
29. Dynamical generalizations of Chowla's conjecture on short averages
30. Elimination of Ren\'e Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem
31. Asymptotic Formula for Biregular Overpartitions
32. Critical Restricted Sumsets at the Boundary $\lvert A\rvert+\lvert B\rvert=p$
33. Prime Plus a Non-Square-Free Integer: An Elementary Approach
34. Transcendence of Montgomery Reduction Factor in the Ring of Integers Modulo Infinitely Large Primes
35. A proof of Sylvester's conjecture
36. The typical size of Hecke eigenvalue sums is $o(\sqrt{x})$
37. Two-term dilogarithms, mixed-base Nahm sums, and Fricke symmetry
38. Ekedahl-Oort strata meeting the supersingular locus
39. Laurent coefficients of Zagier-type zeta function {\`a} la Ishibashi and arithmetic aspects of extended Ramanujan period function
40. The Dynamical Mordell--Lang Conjecture for Relatively \'{E}tale Systems over Products of Curves
41. On the largest prime factors less than $y$ of consecutive shifted primes
42. Algorithms for $p$-rationality and for $p$-saturation of units
43. Algebraic independence of the exponential and Weierstrass $\wp$-functions
44. On the arithmetic of Tate-Shafarevich groups via Kolyvagin's conjecture
45. Optimising Selberg's method for critical zeros
46. On the number of solutions to $S$-unit equations
47. Hecke structure of quaternionic modular forms mod $p$
48. Periodicity and Period-Length Bounds for Browkin $p$-Adic Continued Fractions
49. An extension of algebraic independence of special values for non-lacunary power series
50. Long runs of integers with small prime factors and the divisor function of $n!$
51. A Construction of an Extremal Even Unimodular Lattice of Rank $88$
52. Singular automorphic products and BKM algebras
53. A septic covariant and the Hermite--Joubert problem in degree seven
54. Another proof of the $U^4(\mathbf{F}_p^n)$-inverse theorem
55. Cauchy laws for zeta logarithmic derivatives and stationary Stieltjes transforms
56. Low moments of Hecke eigenvalue sums
57. A lattice family with kissing constant $\tau(\mathcal{L}_n) \ge e^{\sqrt{n}}$
58. Zeros in The Character Table of The Wreath Product of The Symmetric Group
59. Matrices over non-commutative rings as sums of fifth and seventh powers
60. Subset-Sum Density Realization in Locally Finite Abelian Groups
61. Torsion, Betti rank, and small points in semiabelian schemes
62. Thresholds and Fluctuations for Colorful Arithmetic Progressions in Sparse Random Colorings
63. Noether's problem for $A_6$ and $A_7$
64. Growth beyond exponent $3/2$ for convexity and iterated sum sets
65. AKE principles in roughly deeply ramified henselian valued fields
66. Algebraic Structures on Sets of Partitions
67. NP-hardness of ideal lattice problems
68. Geometric realizations of Brauer classes on K3 surfaces from hyperk\"ahler contractions
69. Dynamical Mordell--Lang Conjecture for Higher-Rank Radially Ramified Skew Products

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-14/

1. An adelic approach to the Kudla-Millson lifts over totally real number fields
2. Local-global principles for visibility of lattice points on parameterized curves
3. On the variation of slopes over moduli stacks of Galois representations
4. Critical convergence and Hausdorff measures for generalized Flint Hills series
5. $S_h$-sets in abelian groups
6. A Generalization of S\'ark\"ozy's theorem in function fields
7. Zeros of Quasimodular Forms Defined by Iterated Sums
8. The first moment of quadratic Dirichlet $L$-functions in the even hyperelliptic ensemble
9. Tight universality of $m$-gonal forms with minimal criterion sets
10. Gauss Genus Theory in Characteristic 2
11. Projective Kernels and Replicability in Modular Function Theory
12. Classification of torsion of elliptic curves over quintic fields
13. Large fluctuations of extended Rademacher random multiplicative functions
14. Projection and fibering in groups of bounded exponent
15. Kronecker sequences beyond the torus: nearest-neighbour distances and best returns
16. Iwasawa theory of CM elliptic curves at potentially supersingular primes
17. Kolyvagin's conjecture at non-ordinary primes
18. An asymptotic formula for a cubic moment of $GL_2$ $L$-functions
19. Jacquet--Rallis transfer for GL(2)
20. Quasipolynomial density bounds for $K$-point configurations in $\mathbb{Z}^d$
21. Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
22. Serre's problem on statistics of Brauer symbols
23. Poincar\'e duality for pro-\'etale $\mathbf{Q}_p$-local systems
24. Characteristic Classes of Adelic Vector Bundles and Applications
25. Non-archimedean Monge-Amp\`ere measures for toric metrics on subvarieties of toric varieties

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-11/

1. A New Sparse Algorithm for Polynomial GCD over Integers
2. Sums of distinct divisors of factorials
3. Ordinary 3-Isogeny Graphs and Improvement of Supersingularity Testing for Twisted Hessian Curves over Prime Fields
4. Effective estimates for exponential sums with multiplicative coefficients
5. Rational Approximations for Reciprocals of Multiple Zeta Values and Trivariate Cauchy Numbers
6. A $p$-adic monodromy theorem for curves
7. Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals
8. Log-crystalline representations and $(\varphi, \Gamma)$-modules
9. The irrationality measure of {\pi} is at most 7.101862832357
10. On the bounded-conductor finiteness conjecture in equal characteristic
11. Sharp unconditional moment bounds for products of L-functions
12. Internal congruences modulo powers of $2$ for overpartition tuples with odd parts
13. Generalized Frobenius Partitions Modulo Powers of $2$
14. Bounded asymptotic bases for linear forms
15. Chowla's non-vanishing conjecture over $\mathbb{F}_q(T)$
16. The asymptotic in Waring's problem over function fields beyond twice the degree
17. On the Mahler measure and root distribution of the $Q$-polynomial of links
18. The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square
19. F-theory on K3 surfaces and orthogonal modular forms
20. A dynamic point of view on universality for random matrices over finite local rings
21. Quantitative universality for products of i.i.d. random matrices
22. Rankin--Selberg integrals of opposite conductor--one newforms
23. Divisibility and torsion in higher Chow groups over arithmetic fields
24. Reversibility and its asymptotic counting in Picard group
25. A maximal function field of genus $17$ over $\mathbb{F}_{11^2}$
26. Cusp restrictions and Bunke--Naumann invariants with level structure

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-10/

1. A proof of Hare's $\epsilon$ unfair conjecture
2. The density of long runs of non-$r$-free integers
3. Spectral Algebras of Abelian Cayley Graphs
4. Triple intersections for algebraic curves on the real torus
5. Cyclotomy of symmetric polynomials
6. Effective Euler Sums
7. The addition on totally positive integers uniquely determines the totally real number field
8. Generic Manin-Mumford
9. Regular Arithmetic Functions, Volume I. Theory, Applications, Examples
10. What Does MMLU Actually Measure? A Psychometric Audit of Difficulty Structure in Aggregate Benchmark Scores
11. Models of Elliptic Curves with Maximal 2-adic Image Subject to a Rational 2-Isogeny
12. Integer group determinants for the elementary abelian group of order 49
13. The three Kanade-Russell identities modulo nine
14. From Pythagorean Runs to Pell-Generated Cubic Runs
15. An elementary approach to Sun Kim's general theta function identities
16. Universal norms and de Rham representations
17. Unramified Motivic Alternating Multiple Mixed Values
18. Non-vanishing of symmetric square $L$-functions in the weight aspect
19. Pencils of norm form equations and a conjecture of Thomas, II
20. Diophantine approximation with primes in an arithmetic progression
21. A Counterexample to a Conjecture of Liu and Qian and a Refined Inverse Theorem for Restricted Sumsets in $\mathbb{Z}_p$
22. Inertial multiplicity bounds for two dimensional projective representations and bounds for the number of $\operatorname{PSL}_2(\mathbb{F}_q)$ and $\operatorname{PGL}_2(\mathbb{F}_q)$ number fields
23. Faltings' Isogeny Theorem via Equidistribution
24. Quasi-modularity of symmetric quasi-shuffles
25. Sharp local estimates for smooth numbers
26. On the syntomic regulator of the Hesse cubic curves and $p$-adic hypergeometric functions
27. Integer group determinants for abelian groups of order 24
28. On the Number of Hecke Eigenvalues of Same Sign on $\mathrm{GL}_n$
29. Irreducibility of truncations of the Catalan generating function
30. $B_h$-sets and perturbations in normed vector spaces
31. The algebraic geometry of 3-by-3 magic squares of squares
32. Positivity and Asymptotics for Chenevier's Orthogonal Polynomials
33. Distinguished standard modules for $\mathrm{GL}_{2m}(\mathbb{C})/\mathrm{GL}_m(\mathbb{H})$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-09/

1. Lower bounds for some value sets over finite fields: incidence geometry and Bourgain's group expansion theorem
2. On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences
3. Primes with Restricted-Digit Differences
4. On the classification of small cyclotomic integers
5. On the class number of certain cyclotomic fields
6. A $q$-microscope for mock-theta denominator patterns
7. Infinite-order $p$-adic differential equations for Hurwitz-type Euler zeta functions: Higher-dimensional extensions and uniqueness of bounded solutions
8. The entropy of coclass one and of SmallGroup(729,45)
9. Central non-vanishing of Dirichlet $L$-functions
10. From dimension four to dimension five in the Tate conjecture for abelian varieties over finite fields
11. Lattice point visibility along polynomials has density one
12. Normal Behavior and Periodic Points of a Pseudo-Aliquot Map Associated with the Dedekind Psi Function
13. Mean Values and Normal Order of a Successive-Iterate Ratio of Dedekind's Arithmetic Function
14. Bounds on Whittaker Functions for $\mathrm{GL}(n)$
15. Fields of definition of $p$-torsion points of elliptic curves and their ramification
16. Methods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial Equation
17. Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization
18. Unsupported Cyclotomic Divisors in Three-Prime Integer Tilings
19. Generalized Zeckendorf expansions of the 2nd order
20. A Fricke transformation for cubic-residue eta products of level 13
21. High dimensional Riemann--Roch spaces in linear spaces with small squares
22. Three Irrationality Results for the Dilogarithm: Rhin--Viola and Viola--Zudilin Constructions at $-1/4$, $1/5$, and $-1/3$
23. Maximising the number of solutions to linear equations
24. $p$-adic properties of division polynomials and algebraic sigma functions
25. Upper bounds for arithmetic functions over polynomial values via Chebotarev--Sato--Tate distributions
26. The method of telescoping continued fractions
27. Counting Representations of Quadratic Forms
28. A Proof of Bala's Congruence Conjectures for A158690
29. Parameterized partial theta identities and a unified $q$-difference proof
30. The Normal Form of Smith's Matrices
31. On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases
32. Prime pairs along rays of prime indices
33. On Dynamical Mordell-Lang Conjecture for Split Map
34. Asymptotically optimal packings of arithmetic progressions with prime differences
35. $\vec M$ Versions of Andrews-Gordon Identities Revisited
36. Zeros of Ramanujan-Like Polynomials
37. Residual finiteness and cuspidal cohomology of Picard modular surfaces
38. Sharp Diameter Bounds for Nonnegative Cyclotomic Multiples
39. A pencil of quadratic forms in nine variables with no member of Witt index four
40. The spectrum of $(\xi\alpha^n)$ can be uncountable
41. Equidistribution of small points over finitely generated fields
42. The Artin-Hasse $p$-section: weighted convolutions and $p$-adic recovery
43. Simple critical zeros and distinct zeros of the Riemann zeta-function in short intervals
44. The Fibonacci numbers are not an additive uniqueness set for multiplicative functions
45. Relative $(\varphi, \Gamma)$-modules and $p$-adic differential equations
46. A Lang-Trotter Problem for Non-Geometric Quadratic Inductions
47. Replication Descent and $J$-Finality of Replicable Functions
48. Todd's relation conjecture and binary relations for multiple zeta values in positive characteristic
49. Pascal tiling and congruences modulo N in Pascal's triangle
50. Moments of the Crank Statistic for $t$-Core Partitions and Overpartitions
51. Prescribed Abscissae on Congruent-Number Curves over Simplest Cubic Fields
52. Second derivatives of $p$-adic $L$-functions and the Shafarevich--Tate group of rank-two CM elliptic curves
53. Counting Survivor Sets: Exponential Equivalence with Prime-Admissible Sets
54. Symmetric power L-functions of a weighted hyper-Kloosterman family
55. A geometric Jacquet--Langlands correspondence for Shimura varieties
56. Four explicit continued fractions for values of the Lerch transcendent and the Hurwitz zeta function
57. A Problem on the largest divisor $d$ of $N$ with $d\leq \sqrt{N}$
58. Reduction Modulo Binary Polynomials with Logarithmic Feedback Depth
59. On a problem of Erd\H{o}s and Nathanson related to minimal asymptotic bases of order $h$
60. On the cardinality of the exception set in Littlewood's discrete conjecture
61. Generalizing a Pair of Diophantine Equations
62. The modulo 9 Kanade--Russell identities and their Nahm-sum duals
63. Rational functions over finite fields with Galois closure of genus zero
64. Sharp order-preserving integer models for short additive equalities
65. The Archimedean place is a blurred interval at infinity
66. Coarse moduli of motivic augmentations
67. Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers
68. Polynomial point counts for moduli spaces of curves with marked points
69. The Constant in Thomae-Type Formulas for Eight Points on the Complex Projective Line
70. Microlocalization and singular supports of constructible \'etale sheaves
71. A Uniform Product-Difference Theorem for Dense Subsets of $\mathbb Z^2$
72. External Difference Families Arising from Two or Three Cyclotomic Classes
73. The exponent of harmonic LCM avoidance
74. Solutions to 6 problems in recurrence and Van der Corput sets
75. Logarithmic $A_{\mathrm{inf}}$-cohomology, Part II
76. Proofs of Some Kanade--Russell Mod 12 Conjectures
77. Majorization and additive tuples in $\mathbb{Z}_2^n$
78. A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map
79. On the $a$-number of Fermat type function fields and some of their subfields
80. The range and omitted values of a certain sequence involving the partition function
81. The sharp constant in the Mashreghi-Ransford inequality

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-07/

1. Multiple zeta values in $\lambda$-rings
2. SIC dimension towers via cyclotomic polynomials
3. A counterexample to the Chung-Graham-Spiro gap-set conjecture
4. Hilbert's Irreducibility for $\mathbb{G}_m$
5. Degeneration of monodromy in the theory of Eisenstein congruences for classical groups
6. Numerical experiments on the Hardy conjecture for the Gauss circle problem
7. On multiply induced characters
8. On the Divisibility Relation $\sigma(n)\mid\sigma(n+h)$ and a Generalized Erd\H{o}s--Sierpi\'nski Conjecture
9. Distribution properties of generalized polynomials
10. The Right Edge of the Zero Set of the Fibonacci Zeta Function
11. Lattice point visibility along powers of quadratic polynomials
12. The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains
13. Counting level-raising congruences using modular representation theory
14. Local Jacquet-Shalika integrals and modifying factors
15. Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions
16. F-sets of arbitrary finite width
17. Distribution of points near the origin in the $d$-dimensional Lagrange spectrum
18. Short arithmetic terms express the cardinality of elliptic curves in Weierstra{\ss} normal form over finite fields
19. Cone upgrade for effective equidistribution and weighted Khintchine--Schmidt theorem on fractals
20. Coleman Isomorphisms in Syntomic Cohomology and $\mathrm{THH}$
21. A Log-Free $n^{1/5}$ Bound for Chowla's Cosine Problem
22. Arithmetic Polyhedra
23. Counting sets with given doubling via dimension

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-04/

1. An upper bound for an exceptional automorphism group
2. Perfect numbers, Wieferich primes and the solutions of $\binom{2n}{n}\equiv 2^n \bmod n$
3. Poissonian pair correlations for the three-particle Sutherland model
4. Skolem-Mahler-Lech in rings of positive characteristic: a shorter proof and a multi-dimensional generalization
5. Factorization patterns and fields of definition of $\ell$-torsion points on the Jacobians of genus 3 hyperelliptic curves
6. On lifting representations and actions on curves of the metacyclic groups $C_{p^s}\rtimes C_m$
7. Representation Defects and Cassels Pairings for Congruent Number Curves
8. Resolving a conjecture on permutation polynomials over $\mathbb{F}_{2^n}$
9. Odd denominators in the Lonely Runner spectrum for six speeds
10. Prime-power Diophantine tuples
11. The Klein-V\'elu septic, 2-Division, and modular function fields of level 14
12. The derived set of multiple star polylogarithms
13. The $\mathfrak{sl}_2$-algebra structure of multiple Eisenstein series
14. Supersingular Elliptic Curves Without Inseparable Small Degree Endomorphisms
15. Overcolored Partition $k$-tuples Restricted by Parity of the Parts
16. Arithmetic probability measures
17. The groups $\operatorname{SL}_2(\mathbb{F}_{13})$ and $\operatorname{SL}_2(\mathbb{F}_{19})$ are Galois over $\mathbb{Q}$
18. Galois representations ramified at one prime via relative deformation theory
19. On the exponential sum over squarefree integers
20. Short character sums of inhomogeneous polynomials
21. The subconvexity problem for symmetric square $L$-functions in level aspect
22. Catalan's constant is irrational
23. Some generalizations of Oort's conjecture
24. Connections between colored restricted $b$-ary and ordinary partitions
25. Extension Problems for the Vladimirov--Taibleson Operator and the Hierarchical Laplacian
26. From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra
27. A Fej\'er--Riesz inequality for Dirichlet series
28. The Prime Clockwork: A Dynamic Representation of Modular and Multiplicative Arithmetic
29. Oort's conjecture for split unitary Shimura varieties

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-03/

1. A lower bound for the Call-Silverman height in cyclotomic extensions
2. On the cuspidal cohomology of Iwahori congruence subgroups of $\mathrm{SL}(3, \mathbb{Z})$
3. Ranks and integer points on elliptic curves induced by Fibonacci triples
4. On everywhere locally soluble varieties in families over toric bases
5. When Fibonacci and Lucas Meet Smith: A Computational Exploration
6. Jacquet-Zagier treatment of the beyond endoscopy trace formula for $\mathrm{GL}_2$
7. Summing the reciprocal of the polynomial appearing in Fermat's Last Theorem
8. Bounding Selmer Groups of Superelliptic Jacobians via Class Groups
9. Affine Copies of Three-Point Patterns in Sets of Integers
10. On the counting function of square-full numbers
11. Regularised double shuffle relations for planar Arborified Zeta Values
12. On the Growth of Denominators of Simultaneous Best Diophantine Approximations in the Euclidean Norm
13. Large values of cubic and quartic Dirichlet $L$-functions of prime moduli
14. A Two-Variable Zeta Function for a Parity-Perturbed Hofstadter Q-Recursion: The Exceptional t = -1 Slice and Gaussian Boundary Layers
15. The Hasse norm principle for $A_4$-quartic extensions of global function fields
16. Improved Weyl bounds on short intervals
17. On the occurrence of congruence multiplicities between Ramanujan's theta functions
18. On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function
19. Adelic points and unmramified Brauer approximation for classifying stacks
20. Petersson-Rigid Lattices in a Census of 100 Rank-Three Root Bases
21. A new proof that more than $2/3$ of the zeros of the Riemann zeta function are simple and on the critical line
22. Iterated-sumset spectra: The complete exponent law and its rank geometry
23. Sparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture
24. $\mathfrak{sl}_2$-action on the uri Lie algebra
25. A finiteness theorem for geodesic Leech wheels
26. Fourteen lonely runners
27. Finite extensions of abelian schemes and duality for commutative group stacks

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-02/

1. Reducing Every Set of 36 Consecutive Integers to Zero by Differences of Squares
2. Colombo's Determinant Problem
3. The shortest harmonic sums with decreasing denominator
4. From Common-Slot Chains to Heisenberg Central Products over Global Fields
5. Smooth Diffeomorphisms and Mahler's Problem on Liouville Numbers
6. Almost $k$-th powers in short intervals
7. Exceptional points on Atkin--Lehner quotients
8. Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
9. Distribution of Kaneko's val function
10. A unification of Euler-Maclaurin and Euler-Boole summation formulas
11. Improved bounds in Birch's theorem for forms in many variables
12. Universal murmuration and Hecke augmentation
13. Covering Projective Height Balls by Subspaces in Rigid Adelic Spaces
14. Sharp lower bounds for shifted moments of Dedekind zeta functions
15. Nonabelian Chabauty for the Thrice-punctured Line over Cyclotomic Fields
16. An improvement on the largest prime factor of $n^2+1$
17. New classes of trace-form permutation polynomials and their compositional inverses
18. Regularized spectral expansion of a Rankin--Selberg period and moments
19. Confluence relations for $q$-analogues of multiple zeta values
20. A General Construction of Codes from Drinfeld Modules
21. On the Ramification of Quadratic Fields where there is a torsion growth
22. A Proof of Fraenkel's Conjecture
23. Ten unknowns for Hilbert's tenth problem over the integers
24. The First Two Exceptional Boundaries for Sets with Few Subset Sums
25. Shifted poles and chamber cancellation for classical Witten zeta functions
26. Infinite transitivity of tame groups of automorphisms of affine spaces
27. Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic
28. Deciding superellipticity and computing the Weierstrass normal form
29. Two-photon quantum Rabi models - Spectral degeneracy and symmetries
30. On Algebraic Integrability of Vector Fields with Rational Function Coefficients that Separate Variables
31. Sharp Threshold for Universality of Rational Canonical Forms over a Finite Field
32. $A_1$ - Coulomb branches over finite fields and Selberg Character sums

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-09-01/

1. On weighted forms in many variables
2. Stable Solutions to Generalizations of Fibonacci Relations of Higher Order
3. $q$-Analogues of some supercongruences related to generalized Van Hamme-type supercongruences
4. Counterexamples to O'Neil's Period-Index Problem on Elliptic Curves
5. Vanishing of $\mathrm{Sha}(A/K)[\mathfrak{P}^\infty]$ and its consequences for the anticyclotomic Iwasawa theory of $\mathrm{GL}_2$-abelian varieties
6. The average number of rational preperiodic points of polynomials over $\mathbb{Q}$
7. Analogue of Cardy's formula on the 60-degree parallelogram: a modular approach
8. The Shimura Lift and Hilbert Modular Forms
9. Kato's main conjecture for nonordinary modular forms
10. Lagrange spectrum for Diophantine approximations of complex numbers with real part equal to one half
11. Luo's Spectral Large Sieve Inequality on Short Intervals
12. Bloch-regulator Principal Parts of Cyclotomic Iwasawa Pseudomeasures
13. On the special values of Berndt's generalized $L$-function
14. Counting integral points near a curve in the n-dimensional Euclidean space
15. Wallis-type products with polynomial exponents and the Dirichlet beta function at negative integers
16. Exact logarithmic Hausdorff and capacity exponents of the non-Brjuno set
17. Difference of the modular function $\omega_{2}(\tau)$, revisited
18. Euler Characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$, and their cohomological consequences
19. On supersingular isogeny graphs of Drinfeld modules
20. The arithmetic of critical values II: critical elliptic curves
21. Hecke Subalgebras and Local Newforms for the Metaplectic Double Cover of $\SL_2(\mathbb Q_p)$
22. Average twin prime conjecture for elliptic curves in arithmetic progressions
23. $D(N)$-quadruples in upper-triangular $2\times2$ integer matrices
24. Lower Bounds for Moments of $L$-functions
25. Matrix representations and arithmetic properties of jacobsthal numbers via binary 3x3 matrices
26. Sets whose differences avoid a bracket quadratic
27. Complete characterization of a class of complete permutation quadrinomials over \(\mathbb{F}_{q^2}\)
28. $13$ unknowns over quadratic integer rings and Lucas congruences
29. Relative Langlands duality of the Bump-Friedberg-Ginzburg $\mathrm{GSO}_6$-integral
30. Joint Equidistribution of Subspaces of Bounded Height in Rigid Adelic Spaces
31. Unit Indices of Prime-Index Shanks Orders
32. Density of the multidimensional Lagrange spectrum
33. An Explicit Belyi Map for the Wiman Sextic and Cusp Forms for a Noncongruence Subgroup
34. Reduced polynomial lifts of APN permutations over Galois rings and effective non-APN bounds
35. Normal and Lognormal Asymptotics for Lattice-Point Counts in Random Translates of High-Dimensional Balls
36. Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
37. Subconvexity of Short $k$-Free Exponential Sums in $\mathbb{F}_q[t]$
38. Large zeta sums and zeros of the Riemann zeta function
39. Bounded gaps between primes
40. Quantitative time-averaged spherical means along equidistributed spirals: Diophantine rates and limits of uniformity
41. Lattice Green's function of the hyperkagome lattice: modular uniformization at level 30 from an orthogonal differential Galois group
42. Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection
43. Generalized Jantzen filtration, hyperbolic restriction, and characteristic cycles
44. Pseudo-spherical representations and types for covers of split tori
45. On the Babylonian Division of Trapezoids
46. Recovering Laplacian Lattices from $L$-Functions of Graphs
47. Prime and Touchard Congruences of Mixed-Type Bell Numbers
48. A requested analytic proof of an identity of Dixit, Kumar, and Srivastava

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-31/

1. The Sufficient Set of Congruences of Binomial Coefficients for Primality
2. Finite and Symmetric Multiple $T$-Values
3. Diophantine m-tuples of Triangular Numbers
4. Trilinear Kloosterman fractions II: subdyadic intervals and nearly balanced convolutions
5. An Erd\H{o}s-Wintner theorem for second-order linear recurrent bases
6. The Multiplicative Persistence Conjecture: Resolving the \(2\)-Adic Obstruction for Nonzero Even Targets
7. Drinfeld modular forms of higher rank from a lattice-oriented point of view
8. Generalized Fermat equation over number fields
9. Lattice points in high-dimensional $\ell^q$ balls with small radii
10. Rational and integral values of rational functions at rational points
11. Norm Principles for ${\rm Go}(q)$ and ${\rm Spin}(q)$
12. The Algebraicity Problem for Hard-Core Entropy Constants on the Discrete Hypertori
13. Rational torsion on simple genus two Jacobians
14. Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments
15. Zero-free columns in character tables of symmetric groups
16. On Frobenius rigidity for motivic cohomology
17. On the number of $2$-dice games with prime power dice-size
18. Arithmetic purity of strong approximation for toric varieties with constant global sections
19. Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces
20. On Manin's conjecture for quartic del Pezzo fibrations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-28/

1. Closed geodesics in homology classes modulo sublattices
2. Discrete dynamics of Eratosthenes sieve
3. $k$-Lucas Annulus for Polynomial Zeros
4. A Neighbouring-Denominator Case of the Erd\H{o}s--Mahler Conjecture
5. Period Relations for Theta Products and Elliptic Integral Moments
6. The k-Rank Taylor Family: Canonical Harmonic Lifts, Principal Parts, and Rademacher Series
7. $\mathbb{F}_q$-linear relations among Thakur's multiple zeta values in positive characteristic
8. Torsion-vanishing for Siegel modular varieties via supercuspidal congruences
9. Specialisations of the Burungale-Castella-Skinner main conjecture to $\mathbb Z_p$-lines
10. Two-point correlations of multiplicative functions with dense orbits
11. The Cartesian product of exact approximation sets
12. Ap\'ery-type approximations and irrationality measures for certain $q$-series
13. Resultants of dynatomic polynomials of $x^d$
14. Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension
15. Modular periodicity of the Euler up/down numbers at odd prime powers
16. On variants of P\'olya's conjecture
17. Exceptional covers of the projective line with genus-one Galois closure: arithmetic forms over finite fields
18. The Matrix Pythagorean Equation over $\mathrm{GL}_2(\mathbb{Z})$
19. Birch's theorem over function fields with quadratically many variables
20. On Consecutive Non-primitive Elements over Finite Fields
21. On Piatetski-Shapiro primes from almost primes
22. Integers divisible by a shifted prime in a given interval
23. Delta theory of Anderson Modules II: Hodge-Pink structure
24. Value distribution of multiplicative functions along linear fractional sequences
25. On polynomial expanders with many variables
26. Mixed Tate motives over number fields
27. Isocrystals on unibranch varieties and open immersions
28. The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
29. A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields
30. Hankel determinants of Catalan-like sequences

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-27/

1. On the sum of least prime factors in short intervals
2. Transcendence of Tonelli--Shanks Power Modulo Infinitely Large Primes
3. Jacob's ladders, new classes of sum variants of almost linear formula and corresponding $\zeta$-functionals and $\zeta$-equivalents of the Fermat-Wiles theorem
4. The equality cases $P_t(\mathbb{N})=\tfrac12$ for the deconvolved sum-of-digits measures
5. The uniform Littlewood conjecture fails on a set of positive Hausdorff dimension
6. The divisor function for matrices
7. Pseudonullity for fine Selmer groups over multiple $\mathbb{Z}_p^{d}$-extensions
8. Simultaneous Diophantine approximation on the three-dimensional Veronese curve: the complete Hausdorff dimension story
9. Well and badly approximable sets, and rapid winning
10. An elliptic K3 surface X/Q(t) with Mordell-Weil rank 17, I: Formulas for X and base changes of rank 18 and 19
11. Rigid analytic 1-motives and conjugate uniformization of abeloid varieties
12. Arithmetic theta invariants and arithmetic equilibrium measures
13. A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers
14. The Mixed Second Moment of Quadratic Dirichlet $L$-functions with Prime Conductors
15. Intermediate-Range Estimates for Short Weyl Sums and Waring's Problem with Almost Proportional Summands
16. A Boolean polynomial operator for the Collatz $3n+1$ problem
17. The second moment of twisted modular $L$-functions and Dirichlet $L$-functions at the central point
18. Sharp extremal asymptotics for Cusick's sum-of-digits bias at fixed Hamming weight
19. Introduction to the Birch and Swinnerton-Dyer Conjecture
20. An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms
21. Remarks on Vafa-Witten theory, or how to sit on a wall
22. A Categorical Framework for the Direct Integration of Banach Spaces

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-26/

1. Collapsing Fifty Dilogarithm Arguments to Five Terms over $\mathbb{Q}\bigl(u,\sqrt{4-3u^{2}}\bigr)$
2. Poincar\'e duality in Hida families
3. Fourier Spectral Reciprocity and Canonical Hecke $L$-Functions
4. Geometric Realization of Finite Residue Casimirs and Weil Operators via Szeg\H{o} Kernels
5. Sieve dimension and search depth for the Erd\H{o}s-Straus conjecture, $n \equiv 1 \pmod{24}$
6. Modular Forms Related to Real Quadratic Fields as Traces of Cycle Integrals
7. Winning property of counterexamples to Uniform Littlewood's Conjecture
8. A Buium--Coleman bound for the Zilber--Pink conjecture for curves inside abelian varieties
9. Sums of three powerful numbers
10. Infinite continued fractions with a finite alphabet and their applications
11. Polynomial representatives of finite-field maps: a sharp dimensional dichotomy
12. Fourier Coefficients of the Degenerate Eisenstein Series on Symplectic Groups
13. On the Geometry and Shapes of Rank 2 Log Unit Lattices
14. Permutation and exceptionality of rational functions from equivariant elliptic isogenies over finite fields
15. A dual reformulation of the complex sin^2-algorithm: exact identities, descent, and finiteness
16. Contributions to the theory of the Euler eta function
17. Integral quadratic forms over a ring of $p$-adic integers
18. Weil positivity in compact windows: certified two-sided bounds and a Landau--Widom decay law
19. Metaconjugation and Quadratic Forms
20. Oscillation of partial sums of the M\"obius function and zeros of Riemann's zeta function
21. Quantum Algorithms and Hardness for Point-Count Approximation over Finite Fields
22. The Number of Curves of Genus 2 with a Given Refined Humbert Invariant
23. Asymptotic Rounding Laws for Optimal Thresholds in Secretary Problems
24. Kloosterman sheaves and Bessel functions for generic principal series of finite groups

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-25/

1. A non-abelian large sieve and Artin's primitive root conjecture
2. Rational Points and Brownian Motion
3. Dense ascending waves: A resolution of the Alon-Spencer conjecture
4. How many points has an affine algebraic set in residue classes modulo n ?
5. Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$-adic and $t$-adic Littlewood Conjectures
6. General Stirling-Ramanujan Constants are exponential periods and applications
7. Prime multipliers of order ten: norm spectra, local charts, and selective lifting
8. Coherent sequences of matrix spectra
9. A Classification of Small MSTD Sets in Arbitrary Fields
10. A note on Zlobin's note
11. Uniformity in rational torsion and small points on abelian varieties
12. The strong form of Van der Waerden's conjecture via twisted Chowla
13. The normalized approximation function for multiple zeta-star values
14. Yun's zeta function and the overorder zeta function for Gorenstein cubic orders
15. Kohnen--Ueda local newforms
16. There and back again with Kaprekar 2-cycles
17. On the constant in Klartag's theorem for lattice packings in high dimensions
18. On uniqueness in equivariant Iwasawa theory
19. Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple
20. The Period-Three Secondary Term in the Mean Value of $L(1/2,\chi_D)$ in the Hyperelliptic Ensemble
21. Cyclotomic norm congruences for zeta values and modular $L$-values
22. Generically Ordinary One-parameter Hyperelliptic Families are Dense
23. Orthogonality Defects of HKZ-Reduced Bases
24. On the binary representation of powers of $3$
25. $p$-adic Equidistribution of Special Loci in a Product of Modular Curves
26. Representations with k-generalized Fibonacci numbers
27. Euclidean Rings
28. A deterministic sin^2-type algorithm for complex cubic irrationalities with exact periodicity certificates
29. Extreme values and logarithm laws for toral translations
30. An elementary note on three consecutive powerful numbers
31. On the graded center of $D(G)^c$
32. Quantitative Logarithmic Chowla Correlations Uniformly over Growing Shifts
33. Power-saving bounds for Thue--Mahler and Mordell equations
34. The classification of generalised Kummer surfaces in positive characteristic
35. Admissibility of Bernstein centers
36. Norm-Query Complexity of Algorithmic Problems in Finite-Dimensional p-adic Normed Spaces
37. The Partition Pairing Theorems I
38. MCSI: A Masked Commutative Supersingular Isogeny Key Exchange with Blinded Ephemeral Keys
39. Marshall Quotients of the Rings $\mathbb Z/n\mathbb Z$
40. A motivic derived Fourier transform
41. On the directions occurring in lattice-line coverings of the integer plane
42. The asymptotic behavior of the rectangle partition function $p(m,n)$
43. An Exact Counting Formula for the Mutual Position of Two Plane Conics
44. The Gao-Zhuang conjecture for the Heisenberg group
45. The number of sum-free subsets of lattice cubes

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-24/

1. A note on least primitive roots
2. Polylogarithmic Chabauty--Kim loci over number fields
3. Maximal and minimal curves of the form $y^3=x^{(q^2+1)/2}+x$
4. Euler characteristic of the Selmer group attached to an Artin representation
5. Complete Resolution Of A Family Of Twisted Thue Equations
6. Arithmetic $\mathcal{D}$-modules over Laurent series fields: the relative case
7. Adjoint Closures of Singular Pairs of Quadratic Forms and a Pfister-Type Criterion
8. Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials
9. Anabelian Geometry in Families
10. Sums of products of Kloosterman sums to prime power moduli
11. Almost sure upper bound for sums of random multiplicative functions and critical chaos
12. On nearly consecutive sequences without long arithmetic progressions
13. A new lower bound for two-color van der Waerden numbers

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-21/

1. Totally positive field extensions and the pythagorean index
2. An Algebraic Approach to the Fundamental Theorem of Algebra
3. Many Representations as Sums of Three Prime Cubes
4. ${}_5F_4$ evaluations and a family of $\pi^2+\log^2$ identities
5. On the Finiteness of Isolated $j$-invariants for $X_1(N)$
6. Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
7. Arithmetic partial differential operators on ramified extensions of $\ZZ_p$
8. Forced Shadows of an Obstructed Hyperbolic Kac-Moody Denominator
9. Ribet Points, geometric divisibility sequence and order of reductions on semiabelian varieties
10. The irrationality measure of arctan1/2 is at most 8.585166
11. Gap spectra and densities of slow Fibonacci walks
12. Exceptional sets for compositions involving Euler's function,the divisor-sum function and Dedekind's function
13. Simultaneous approximation to pairs of real numbers
14. Modularity theorems for Eisenstein congruences in prime-power level
15. Variation of Iwasawa Invariants for Ordinary Representations
16. Simplex--center configurations in dense subsets of Euclidean spaces and the integer lattice
17. On the number of solutions of systems of diagonal equations through diagonal GP-graphs: the general and the Hermitian-form cases
18. Non-equivalence of pro-$p$-Iwahori invariants
19. Spectrum of the refined Diophantine exponent
20. The arithmetic de Rham stack
21. The Local Langlands Correspondence for Middle Supercuspidal Representations of $p$-adic $\text{GL}(2n)$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-20/

1. On sums of two primes and six Fibonacci numbers
2. Properties of Kloosterman sums for long Weyl element on GL(n)
3. Rational Solids with Equal Surface Area and Volume
4. Sharp Transitions for Localized Solutions to a Diophantine Inequality
5. Mean Value Estimates for a Real-Exponent Analogue of Waring's Problem
6. Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces
7. On $p$-adic solubility of $Ax^\ell + By^m + Cz^n = 0$
8. Hecke-type action on higher order Herglotz-Zagier function
9. On the Diophantine Equation $p^x+ (2p+1)^y =z^2$ with Consecutive Exponents
10. A Positive Proportion of the Reduced D'Arcais Polynomials is not Hurwitz
11. Universal Ramanujan-type congruences for prime-detecting quasimodular forms
12. The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers
13. On a classical zero-sum invariant
14. Matchings and product growth in modular abelian independence groups
15. On a conjecture on the Kasami APN function: reductions, structure theorems, a proof for $k\bmod n\in\{1,2,n{-}2,n{-}1\}$, and exhaustive verification for $n\le 13$
16. Finding suitably generic points on curves with an application to the construction of rigid real closed fields
17. Spectral convergence of hyperbolic surfaces and quantum ergodicity
18. Lonely Runners over Function Fields: Quantized Phase--Riesz product
19. Products of trees and ${\rm PGL}_2$-torsors over the punctured affine line
20. Complexity-sensitive additive energy and off-diagonal Young inequalities on bounded-degree algebraic varieties
21. Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery
22. A simple construction of the automorphic residual spectrum
23. A random walk on p-groups with a symmetric perfect pairing

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-19/

1. Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers
2. Algebraic Lattices Arising from Congruence Submodules in Subfields of $p$-th Cyclotomic Fields
3. Mild p-Class Tower Groups of Imaginary Quadratic Fields
4. On Buzzard's Theoren
5. Shifted second moment of Gaussian Hecke $L$-functions $L(s,\lambda^k)$
6. A central limit theorem for prime geodesics on random surfaces of large genus
7. Ribet bimodules and principally polarized superspecial abelian varieties with quaternion action
8. Alternating generalizations of Mizuno's product formula via modified gamma functions
9. Infinitely many primes with a fixed Frobenius field for an elliptic curve over $\mathbb{Q}$
10. On the p-adic Wirsing problem
11. On the integral $2$-adic Tate module of elliptic curves
12. Principal nonsingularity of the Fourier matrices of orders \(70\) and \(143\)
13. Intersecting families and nonvanishing multivariate polynomials over finite fields
14. Squarefree polynomials with missing digits
15. Products of point counts of higher genus curves over finite fields
16. On the Hidden Pascal Symmetry and Moment Constraints of Vector Representatives in Quebbemann's 64-Dimensional Lattice
17. Asymptotics of the Tchoukaillon array and a conjecture of Beluhov
18. A Kernel-Checked Exclusion Certificate for Erd\H{o}s Problem 647

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-18/

1. A descent-set obstruction for the Casas-Alvero conjecture
2. Exponential sums over primes
3. Reciprocity for The Short Twisted Second Moment of The Riemann Zeta Function
4. Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms
5. Transcendence of continued fractions over function fields and a quantitative version of Uchiyama's theorem
6. Algebraic geometric framework of Rogers--Ramanujan identities
7. Interlacing for zeros of the Serre derivative of Eisenstein series
8. Positive quasimodular forms and the sign uncertainty principle
9. Singular-weight Conway-invariant Jacobi forms of index four
10. Proof of a Conjecture on Primitive Quartic Polynomials over Finite Fields
11. Formal finite multiple zeta values
12. Cycles of supersingular elliptic curves for pairing-based proof systems
13. Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 5: cancellation theory
14. The principal series 2-representation for $\mathrm{GL}_n\times\mathrm{GL}_n$ over a 2-dimensional local field
15. An exact formula for Erd\H{o}s' problem 1005
16. Hausdorff dimension of $\tau$-approximable points on self-similar sets in $\mathbb R^d$
17. Large values of quadratic character sums
18. Better than square-root cancellation in Piatetski-Shapiro sequences
19. Weighted singular vectors in common-base self-similar sets
20. On the Hausdorff dimension of the difference sets between typical and normal numbers
21. Height Rigidity for Entire Functions
22. On integers that are representable as the sum of two units
23. On the residual Eisenstein cohomology of unitary groups
24. Simple and distinct zeros in a prime-modulus Dirichlet family at mesoscopic shrinking height
25. Superspecial Points on Shimura Curves
26. A dynamical generalization of Chowla's conjecture on average
27. The multiplication table problem in large dimensions
28. Oort's conjecture on supersingular abelian varieties in odd characteristic
29. Subconvexity of Short $k$-Free Exponential Sums
30. Galois descents of certain multiple polylogarithms
31. M\"obius Covariance and Coefficient Duality: From Bernoulli Series to Enumerative Applications
32. The equality between the Erd\H{o}s-Ginzburg-Ziv constant and the short product-one constant for finite nonabelian groups
33. A six-functor formalism for syntomic cohomology
34. Degrees of Genus-Two Split-Jacobian Loci and Humbert-Form Reconstruction
35. Matrix group $\Lambda$-distributions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-17/

1. On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian Ranks
2. More than two thirds of the zeta zeros are simple and on the critical line
3. Some Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula
4. $p$-numerical semigroup of the sequence of consecutive odd integers
5. A structural trace identity and certified spectra for the Richelot-Brandt graph
6. A Kubilius model for sieve-theoretic sequences
7. Ratio of sum of digits functions in two bases
8. Hurwitz class number relations and mock modular forms
9. New Congruences Involving $p$-adic dual sequences
10. Shimura curves of discriminant 14 and 15 and associated Heun Functions
11. The inverse Galois problem of iterated Galois groups and their fixed-point proportion
12. Intensional semantics for comparison problems in arithmetic geometry
13. Multiplicative chaos from random multiplicative functions
14. Algebraic curves admitting automorphism groups of large prime square order
15. Sharp refined-direction Kakeya estimates in finite Heisenberg groups
16. Counting non-attracting subtrees and the equidistribution of repelling points
17. Semi-abelian reduction of Albanese varieties
18. Near diagonal additive energy bound for points on algebraic surfaces
19. Compressive Domains and a Bound for the Number of Components of the Fixed Locus of a Self-Map of the Berkovich Line

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-14/

1. On Waring--Goldbach problem with mixed powers
2. Generalized Addition Theorems for the Jacobi Elliptic Functions
3. A conditional arithmetic obstruction to the prime numbers as a spectrum of a probability measure
4. Finding all cospectral mates over a number field
5. Special Values of Shifted Dirichlet Series from an Adjoint Map on Almost Holomorphic Modular Forms
6. Density bounds for permutations avoiding monotone arithmetic progressions
7. Escalations and criteria over real quadratic fields
8. Algebraic constructions of point sequences with quasi-uniform two-dimensional projections
9. Uniform bounds on prime levels of abelian division fields of elliptic curves over number fields without rationally defined CM
10. Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors
11. On the Lorenz-Fibonacci sequences and substitutions
12. Cyclic permutations of large subsets with polynomial values in multiplicative subgroups of finite fields
13. A study of degenerate Bernoulli and Euler numbers via operators
14. Analytic rank one propagation in Hida families
15. On $\mathcal{B}^4$-almost periodicity for a class of arithmetical functions
16. Generalizations of the Christoffel-Darboux formula and congruences involving Ap\'ery-like numbers
17. Infinitely many elliptic curves over $\mathbb{Q}(i)$ of exact ranks 4 and 6 with $j$-invariant 1728
18. Asymptotic Analysis and Phase Transition of the Bessel-Kuznetsov Transform with an Oscillatory Phase
19. On a conjecture of Corradi and Katai
20. Convolution-type Bombieri-Vinogradov theorem with well-factorable Weights, and its applications
21. Local Minkowski units in non-abelian extensions with cyclic Sylow $p$-subgroups
22. Some convolution identities for mock modular forms arising from the theory of holomorphic projection
23. Gross vectors modulo 2 and elliptic curves of prime conductor
24. Intersective Polynomials and Universal Separation of Divosor Profiles
25. The distribution of $k$-free ideals in ray class groups
26. Multiplicative Subgroups of Prime Fields Are Not Sumsets
27. The Five Distance Theorem For A Convex Norm
28. Tame fundamental groups of rigid spaces
29. Euclidean SVP is deterministically NP-hard to approximate within any constant factor
30. Spectral and Isoperimetric Bounds on Flat Tori
31. Optimal local convergence criteria for integer and Gaussian integer continued fractions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-13/

1. The motivic Selmer scheme of the thrice-punctured line
2. Upper bound for the moment of shifted values of cubic $L$-functions over function fields
3. Galois Symbols for a Jacobian and Multiplicative Groups
4. Equalities among simplest quartic fields: a complete classification
5. Height lower bounds for elements of highly composite rings
6. A $p$-part Birch and Swinnerton-Dyer Formula over Totally Imaginary Quadratic Extension of Totally Real Fields
7. Hasse-Witt invariants for trace forms of Jacobi polynomials
8. Duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values
9. The 196560 auxiliary-function conjecture for the Leech lattice
10. Multiplicator freeness for restricted-ramification Galois groups over global function fields
11. Power sums and Siegel-type zero-free regions for L-functions
12. A Multiplicative Fourier Proof of the Length-Four Index Conjecture
13. On The Spectral Properties of Discrete Landscape Functions
14. Visible Measures along $\Omega(n)$ and Distribution of Horocycle Orbits
15. A Proof of a Conjecture on Fixed Perimeter Partitions
16. Edit distance exponents for irrational rotations
17. Invariant Functions on $p$-divisible Groups and the $p$-adic Corona Problem II
18. Near optimal three-fold additive energy bound for points on convex curves

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-12/

1. On the Squarefree Values of Degree-$2q$ Polynomials
2. An omega result for the first sign change of coefficients of symmetric power $L$-functions of Hecke-Maass cusp forms
3. A proof of a weighted sum conjecture for finite multiple zeta values of level two
4. Average root numbers in two isotrivial families of elliptic curves
5. Permutation polynomials from the trace functions
6. Bockstein Spectral Sequences and Applications to the Tame Fontaine Mazur Conjecture
7. Distinguishing elliptic curves modulo $p$ and identifying images of product representations
8. A canonical construction of signed $p$-adic $L$-functions for non-ordinary modular forms of weight $\leq p+1$
9. Equationless quadratic Chabauty for non-split Cartan modular curves
10. A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums
11. Kneserized Anticoncentration and Reverse Absorption for Graham's Rearrangement Conjecture
12. Classification of Fourier summation formulas on a horizontal strip
13. Introduction to Universal Equations and Characteristic-free Resolution
14. Mutation-preserving generalized cluster algebras and Laurent mutation invariants
15. Finite monodromy groups in degenerating families and the stability degree of curves
16. Poincar\'e \`a la Makdisi

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-11/

1. Zeta zeros of function fields heuristically equidistribute as genus goes to infinity
2. Sharp vertex connectivity of the Markoff graphs modulo $p$
3. Positive Lower Density for Hofstadter's $ab-1$ Problem
4. On the Emerton-Gee stack of potentially semistable representations
5. Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures
6. Which numbers are $u$-invariants of perfectoid fields?
7. Binomial coefficients coprime to 6
8. Short Second Moment of $\mathrm{GL}(2)$ L-Functions via Trivial Delta
9. Equidistribution for semiabelian varieties over number fields
10. Machine-Guided Recurrence Boundary Theory for Nahm Sums
11. On Sun's Conjectures for Truncated Jacobi-Symbol Determinants via Supersingular Elliptic Curves
12. Proofs of the Conjectures on $SOME(n)$ and $DSOME(n)$ Functions Related to Integer Partitions
13. The Mathieu group $M_{23}$ is a Galois group over $\mathbb{Q}$
14. A new hyperbolicity wedge and a joint semicircle limit for Jensen polynomials of Riemann's $\xi$-function
15. Twisted Bernoulli Zeros in Quasi-Linear Time: Distribution, Depth, and Explicit Hilbert Class Components
16. On some representations of Metacyclic groups whose integral forms can be computed from a single residual representation
17. Modular resurgent structures for vectors
18. Sharp Bounds for Rational Points Near Space Curves
19. The minimal obstruction modulus for quadratic forms
20. Plancherel and Poisson summation formulae for a family of affine $\Psi$-bundles
21. A Sharper Explicit Result for the Sum of Two Almost Primes
22. A proof of a conjecture on permutation polynomials
23. An analogue of Hirose's relation for finite multiple harmonic $q$-series at roots of unity
24. Counting metacyclic fields
25. On the $\beta=2$ Partition function for Dirichlet $L$-functions in the $q$-aspect
26. Large class of many-to-one mappings over quadratic extension of finite fields
27. Uniform stratified vanishing and equidistribution on $\mathbb{G}_m^d$
28. On the Godement-Jacquet functional equation for finite matrix monoids
29. The Borel complexity of non-Archimedean operator ranges
30. Some new results for Andrews' Kimberling partitions
31. Hankel Transform and $(\alpha,\beta)$ Somos-4 Sequences
32. Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples
33. A note on the partition function of a rectangle
34. Restricted generalized Schur numbers
35. Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages
36. A proof of the cyclotomic conjecture and the non-existence of almost Moore digraphs
37. Varieties with prescribed fundamental group schemes

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-10/

1. Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers
2. Squarefree numbers in short intervals: explicit and formalized
3. Anticyclotomic Iwasawa theory of CM elliptic curves at ramified primes
4. A Combinatorial Approach to Vorono{\"i} Theory
5. An extension of Ramanujan-Guinand identity for the Dedekind zeta function and a new formula for $\zeta_\mathbb{F}(2)$ and $\zeta_\mathbb{F}(2m+1)$
6. On semi-stable integral models for Shimura varieties
7. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture
8. Towards the Fontaine--Mazur conjecture for GL(2)
9. Heath-Brown identities for fractional powers of $\zeta$
10. On the Existence of Primitive Polynomials $f(x)=g(x)+ \lambda$ over Finite Fields
11. Siegel zeros and small gaps between zeros of the Riemann zeta function
12. $\Delta$-separated Sidon sets in additive number theory
13. Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method
14. A three-dimensional corner configuration involving the Omega function
15. Arithmetic Properties of Mixed Stirling Numbers of the second kind

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-07/

1. Rigidity of Averages over the Two Largest Prime Factors
2. Explicit Algebraic Numbers all whose Integer Parts of Powers are Composite
3. The sesquicentennial of the prime number $2^{127} - 1$
4. Trianguline representations and locally analytic principal series of ${\rm GL}_2({\mathbb Q}_p)$
5. Asymptotic uncorrelations between functions with squarefull kernel and functions of invariant average
6. Modularity of Point Counts for the Curves $X^a=Y^b$: New Rogers--Ramanujan Identities
7. Iwasawa invariants and exceptional pairs of certain abelian fields
8. Generalised Gauss--Kuzmin Distribution for Klein sails in $\mathbb R^3$
9. Hearing Tamagawa Factors modulo $q - 1$
10. Hybrid Weyl Subconvexity over Imaginary Quadratic Fields
11. Bounds for moments of twisted quadratic characters of prime modulus
12. Periods of E-operators
13. Strong Weil Degree Divisibility at Higher Levels
14. Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$
15. The good reduction of generalized Kummer surfaces in the non-supersingular case
16. On the motivic cohomology of some singular rings
17. New central $q$-binomial identities
18. Higher-Order Cyclotomic Congruences for $q$-Secant and Generalized $q$-Euler Numbers
19. Exact renewal laws for minimal common-denominator profiles in simultaneous Laurent-series approximation

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-06/

1. Rational spanning sets of level-one cusp forms from Eisenstein series at prime levels
2. The distribution and the structure of the maximum of partial sums in families of trace functions
3. The $5$-divisible integer group determinants for the elementary abelian group of order 25
4. On the Burgess bound and Pythagorean triples involving primitive roots
5. Powers as Fibonacci Sums
6. Regularized Multitangent Functions and Reduction Theorem
7. Construction Of Non-Odd Galois Representations With Large Image
8. On the $L^2$ restriction norm of large level
9. A proof of the Freiman-Lev conjecture
10. Adelic framed form class groups and explicit class field theory
11. Quantitative Khintchine on the parabola with non-monotonic approximation functions
12. Chebotarev geodesic theorem: non-split case
13. An Integral Mean Value Theorem for Weyl Sums over Broken Arcs
14. Weyl Subconvexity for $\mathrm{GL}_2$ with Simple Supercuspidal Ramification
15. Dualizable Additive Categories
16. Sparse Random Covers and Growth of Torsion in First Homology

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-05/

1. A Classification of Multiply Monogenic Quartic Orders
2. Counting in Vieta graphs over $\mathbb{F}_p$
3. On pairs of primes with small order reciprocity
4. Admissible Pairs: A Variation to Pollock Conjectures
5. Mellin Transform Formulas for Anderson Modules and Hints of Modularity
6. Erd\H{o}s-Moser Equation in Arithmetic Progressions
7. Explicit Jordan decompositions for ideal lattices in CM fields
8. No three algebraic conjugates of degree sixteen sum to zero
9. An upper bound for counting algebraic tori over $\mathbb{Q}$ by Artin conductor
10. On the distribution of $\phi(\psi(n))$ and $\psi(\psi(n))$
11. Non-split Cartan curves and a characterization of fake elliptic curves
12. On Diophantine equations over the integer rings of quadratic fields
13. The extended Fargues--Scholze spectral action
14. Murphy's law in non-abelian Hodge theory
15. Strichartz estimates for quasi-periodic functions on long time intervals: An arithmetic approach
16. Refined upper bounds on Schur-like numbers

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-04/

1. Random Multiplicative Functions with Periodic Weights
2. Ljunggren--Jacobsthal and Bailey-Type Congruences for Rectangular Gaussian Binomial Coefficients
3. Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields
4. Positive rational series for reciprocal powers of Catalan's constant and Dirichlet beta values
5. Negative bias in moments of the Legendre family of elliptic curves
6. Machine learning the arithmetic of Boyd's Mahler measure conjectures
7. Faster Deterministic Integer Root Finding for Integer Polynomials
8. Dynamical Canonical Heights and Finite Trees
9. The Minimal Degree of Salem Numbers with Negative Trace
10. Cycles for Rankin-Selberg $L$-functions, I: automorphic periods
11. de Rham theory and locally analytic vectors
12. Arithmetic of elliptic curves induced by regular Diophantine triples
13. Lattice point sumsets and asymptotic approximate groups
14. Weights in \'etale cohomology over mixed-characteristic local fields and applications to anabelian geometry
15. Bilinear Kloosterman sums over small boxes and uniformity of a random walk
16. Distribution of simplices in the discrete and continuous settings
17. On binomial order and primitivity of irreducible quadratic polynomials over finite fields
18. Murmurations of quadratic and cubic characters over function fields
19. Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$
20. Families preserving isomorphisms via techniques in anabelian geometry: with an application to a generalized Neukirch-Uchida theorem
21. Nine-distance theorem and growth of best-approximation denominators
22. A Coates-Sinnott-type Theorem for First Derivatives of Artin $L$-Functions
23. Bounds for Mertens Sums
24. Algorithmic universal \'etale $(\varphi,\Gamma)$-modules
25. On the Petersson norm $\langle\theta_{\psi},\theta_{\psi}\rangle$
26. Constructing Self-Regulating Field Theoriesfrom Primal Wave Fields without Background Manifolds:The Emergence of the Coordinate Continuum
27. A New Characteristic-Uniform Model for Elliptic Curves -- Theory, Arithmetic, and Applications
28. Factorial residues modulo a prime: beyond the square-root bound
29. Integral Representations and Asymptotics for a Family of Areal Mahler Measures
30. The Local Four-Square Problem over \(\mathbb{Z}_{p^k}\)
31. Every quasiperfect number has at least eight distinct prime factors
32. Multiple Zeta Values
33. On the $L^6$-norm of holomorphic Hecke eigenforms
34. Mahler measures at interior CM points: proofs of two conjectures of Samart
35. Samart's conjecture n_4(81)=40M_7: the exact CM evaluation and the two obstructions. A status report
36. An intermediate conjecture between Goldbach and Dubner: every even number is the sum of a prime and a twin prime
37. Isogeny graphs of elliptic curves in characteristic zero
38. Automorphic functions for square-zero extensions of curves over finite fields
39. Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
40. Associated graded modules for modular representations of quaternion algebras
41. Identities involving the number of missing integers in partitions - combinatorial proofs
42. Localization and elliptic motivic relations
43. Fixed Perimeter Analogues of Several Partition Results Related to Parity
44. Arithmetic hypergeometric $\mathcal {D}$-modules and exponential sums on reductive groups
45. The finitude of the fibers of the complementary Bell numbers
46. Collinear Interior Lattice Points in Triangles Satisfying $B(T)\in\{4,5\}$
47. Convolutive sequences, II: Parametrizations
48. Schur--Plucker Geometry of the MDS Locus for Principal-Ideal Codes
49. Square-Difference-Free Sets beyond the Three-Quarter Barrier
50. Intertwining Operators for Siegel Parabolics over Finite Fields
51. The catenary degree of monoids of product-one sequences
52. Square-integrability of holomorphic differential forms on locally symmetric varieties
53. Counterexamples to the Minimum Period Conjecture for Restricted Partition Functions
54. Comparing local-global obstructions on algebraic stacks

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-08-03/

1. Multiplicative dependence in the sumset of multiplicative groups
2. The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of $-1 \pmod N$
3. Small points in radical extensions of number fields
4. Generalized Wieferich primes and monogenic trinomials
5. An Introduction to p-adic Hodge Theory
6. A sharp almost sure upper bound for partial sums of random multiplicative functions
7. On the size of $h$-fold sumsets
8. The least quadratic residue and integers represented by quadratic forms
9. On Generalized Chebyshev polynomials
10. Slice and Partition Rank Criteria for Polynomial Zero-Avoidance

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-31/

1. The exceptional set of the Goldbach problem
2. Multivariate counting of wild abelian extensions
3. On some Diophantine and Ergodic properties of the Schneider map over function fields
4. On the greatest common divisor of $n, \lfloor \alpha_1n\rfloor, \lfloor \alpha_2n^2\rfloor, ..., \lfloor \alpha_kn^k\rfloor$
5. An Asymptotic Bound for Non-covering Congruence Systems over Fq[x]
6. Perfect $2$-codes over arbitrary alphabets
7. Schur Eisenstein series and Schur MacMahon series
8. Irrationality of finite logarithms in a congruence-class ad\`ele ring
9. On a question of Gowers related to Littlewood's conjecture
10. On the Gow--McGuire Conjecture for Primitive Quadratic Polynomials
11. Random linear configurations in dense sets and primes
12. Regularity of Diophantine quadruples over $\mathbb{Q}(i)[X]$
13. Euler-type Recurrence Relations for Partition Functions with Congruence Conditions
14. Eventually greedy best Egyptian underapproximations of rational numbers via optimal control
15. Ginzburg's conjecture on the unramified computation of Eulerian integrals
16. Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of $\operatorname{PGL}_d$
17. Deformation of the absolute Galois groups of number fields
18. Schwartz spaces on L-monoids: non-Archimedean
19. Sumsets and generalized arithmetic progressions in multiplicative subgroups
20. $\mathbb Q\setminus\mathbb Z$ is diophantine over $\mathbb Q$ with $7$ unknowns
21. Proof of a Conjectured Ramanujan Type Master Theorem for Powers of the Cosecant
22. Types and collapse for cuspidal representations of groups acting on trees
23. Franklin's identity for $n$-color partitions and companion Beck-type identities

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-30/

1. On purity of Anderson t-modules
2. Inclusions between p-bounded crystalline loci in dimension two
3. Bhargava Gamma functions for determinant-admissible sets
4. On the transcendence of twisted special $L$-values at non-negative integers in characteristic $p$
5. Improved Bounds for Distinct Multiples in Intervals
6. On Oliver's relations between infinite series and infinite products
7. On a Question of Lehmer concerning the Comtet Numbers
8. On the higher algebraic $K$-groups of arithmetically equivalent number fields
9. Explicit mock Heegner points and BSD formula on certain Mordell curves
10. Dimensions of Orbit Closures and Discrepancy for Dynamical $p$-adic Sequences
11. Kuroda's Class Number Formula
12. On a problem of minimal additive complements for not eventually periodic $S$-difference sets
13. On the second moment and non-vanishing of central values of Hecke $L$-functions of $r$-th order characters
14. Formally certifying number field invariants
15. Fuglede's Conjecture on Cyclic Groups of Square-Free Order: The Case of Rapidly Growing Prime Factors
16. Asymptotics of the spectral determinant of the weighted Laplacian for a sequence of compact Riemann surfaces of infinitely growing volume
17. Splitting Brauer classes by genus one curves over number fields
18. A topological interpretation of numbers

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-29/

1. Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist
2. Transcendence of multivariate Mahler functions and algebraic relations between their values
3. Twisted automorphic descent to odd GSpin groups and applications
4. On certain $D(9)$ and $D(64)$ Diophantine triples
5. The Explicit Hypergeometric Modularity Method III
6. Diagonal cycles on Shtukas and the adjoint $L$-function
7. On the Vanishing of the Brauer-Manin Obstruction for Normic Bundles
8. Beyond endoscopy for the symmetric square representation: The simple trace formula case
9. Extreme values of quadratic Dirichlet $L$-functions with prime-related moduli
10. On an asymmetric additive energy inequality
11. Hypernatural numbers in arithmetic Ramsey theory
12. Refined Humbert Invariants in Supersingular Isogeny Degree Analysis
13. An Asymptotic Formula in Waring's Problem for Seventeen Fourth Powers with Almost Equal Summands
14. Multiplicative subgroups are not restricted sumsets
15. Intersection Cohomology of Igusa Stacks
16. $d$-Translated Unit Sensitive Primes
17. Collision of Orbits for Families of Polynomials Defined over Number Fields
18. Local Moments of M\"obius Fourier Polynomials and the Riemann Hypothesis
19. A Criterion for Equidistribution along the $\Omega$ Function over Polynomial Sequences with Applications
20. Graph integrals, Feynman periods, and single-valued multiple zeta values
21. Kernel-Checked Exclusions for the Erd\H{o}s-Selfridge Odd Covering Problem: Any Odd Covering of $\mathbb{Z}$ Has lcm Exceeding 10000
22. Solution of Erd\H{o}s problem $\# 443$
23. Iterate Wronskians over $\mathbb{R}^d$ as $N$-ary brackets on $\mathbb{R}[x^1,\ldots,x^d]$: the $N$-bonacci numbers bound the highest total degrees

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-28/

1. Jittered sampling and probability measures
2. Tadpole Nahm sum as a Wronskian
3. Unshared zeros of Dirichlet $L$-functions
4. On the Frobenius Number of Quotients of Numerical Semigroups
5. Finite length for unramified $\mathrm{GL}_2$: beyond multiplicity one, non-semisimple case
6. On the role of higher roots in prime ideal races
7. Explicit Twisted Hilbert Class Components Beyond Classical Irregularity
8. On the Comparison of the D-new Modular Degree and the Shimura Degree of Modular Abelian Varieties
9. Modularity of Nahm Sums Dual to Zagier's Rank-Three Examples
10. A lower bound for the distance between CM points on Shimura curves
11. Matrix Kloosterman sums and product-trace estimates for semisimple algebras
12. On the automorphisms of numerical power monoids
13. Optimality of Wouter van Doorn's Upper Bound for the Mayer-Erd\H{o}s Farey Problem
14. Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search
15. Algebraic values of transcendental power series with geometric coefficient moduli
16. Larger sieve with height function and uniform bounds for integral points on curves over number fields
17. Slowly Divergent Trajectories for Weighted Singular Vectors in R^2
18. Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
19. Signs of Square-Free Fourier Coefficients of Half-Integral weight cusp forms and the Congruent Number Problem
20. Bilinear forms with Kloosterman sums via quadratic characters
21. On $C^k$-functions mapping $\mathbb{Q}$ into itself and Mahler's problem on Liouville numbers
22. A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles
23. Non-isomorphism of rings of integer-coefficient holomorphic functions on disks of varying radius
24. Tiling a triangle into a prime number of congruent triangles
25. Additive Bases from Primitive Dyck Words: Regular Underapproximations, Motzkin Coding, and Digit Lifting
26. On the Thickness of Infinite Generalized Sidon Sets, II
27. Beyond the Adams Conjecture
28. Cyclic codes and cyclically covering subspaces
29. Multiplicative irreducibility of shifted multiplicative subgroups in the extremal case
30. Simply branched covers of curves and wild conductor exponents
31. On the problem of large gcd for disjoint residue classes

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-27/

1. Explicit bounds for Buchstab's function
2. A More Efficient Algorithm for Finding the Number of Permutations of $\mathbb{ZZ}/n\mathbb{ZZ}$ with Distinct Partial Sums
3. Factorial Calculi and the Canonical Stirling Defect of the Prime Bhargava Factorial
4. Densities of arithmetic Hecke triangle group orbits
5. Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$
6. Prime-Interval Algebras
7. Congruences for the coefficients of MacMahon-like $q$-series
8. Playing with additivity conditions in multiplicative functions
9. Autonomous disproofs of the sum-product conjecture over $\mathbb R$ with GPT-5.5 Pro
10. Exterior power sums
11. Some aspects of the spectral theory with twisting representations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-24/

1. A problem on sumset sizes of sets of lattice points
2. Infinite Sidon-type sets for zero-sum linear forms
3. Inverses of Fibonacci and Lucas Numbers via Rational Indices
4. Zeros of the Dirichlet series of even zeta values
5. On a Diophantine Equation with Jacobsthal and Fibonacci Numbers
6. Murmurations of quadratic Hecke $L$-functions of the Gaussian field
7. On $v_2(q),v_3(q),v_4(q)$, and Andrews' Conjectures 5 and 6
8. On structured cosine sums and applications
9. Fibonacci, Dirichlet, and Gauss in a single sum
10. The $p$-rationality of $\mathbb{Q}\left(\sqrt{-(kp+m)}\right)$ and $\mathbb{Q}\left(\sqrt{p(p+1)}\right)$
11. On the Fractional Parts of Polynomials Modulo $p$
12. Zeta functions of $\mathrm{PGL}_n$ over non-Archimedean local fields
13. A Weighted Sum Formula for Double Eisenstein Series
14. Statistical properties of Hecke correspondences
15. Simultaneous non-vanishing of Dirichlet $L$--functions, II: Weighted central limit theorem
16. Absolute minimum of a height associated to a semipositive adelic line bundle
17. Generic ordinarity for abelian coverings of the projective line
18. Arithmetic progressions in a random set on a budget

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-23/

1. Integral magneticity of the level-two K3 packet: CM theta lifts and a 2-isogeny trace contraction
2. Additive and multiplicative densities, prime valuations and symbolic models
3. Multiplicative dependence modulo subsets
4. The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves
5. On the value distribution of the Riemann zeta-function with general shifts
6. Extreme values of quadratic Dirichlet $L$-functions
7. Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points
8. Rational Spectra for Finite Hadamard Pairs and Bounded Spectral Sets on the real line
9. The Significance of Proposition II in Galois' M\'emoire, The Origin of Galois Automorphisms
10. The inverse problem for the Steiner-Wiener index of trees
11. Automorphism groups of curves with simple Jacobians
12. The sharp exponent for the minimal distance problem

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-22/

1. On a certain arithmetic function defined via Bernoulli numbers
2. Binary quadratic forms and elliptic curves with analytic rank one
3. Divisor moments of polynomials in Fourier coefficients of modular forms
4. On Diophantine $m$-tuples related to primitive elements of finite fields
5. On the digits of the sum of proper divisors
6. A Distinct Covering System with Minimum Modulus 7 and Minimal Least Common Multiple 10080
7. On canonical roots of fractional ideals
8. On the $\mathcal{A}$-transcendence of a Champernowne-type constant
9. Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap
10. Cyclic and Constacyclic Codes Over Z4+iZ4
11. A Local Classification of Four-Element Multiple Sumsets
12. Zero-cycles on surfaces dominated by products of hyperelliptic curves
13. Generic polar divisors and flag residues for root-system zeta functions
14. Bayesian Sequential Quantum Amplitude Estimation for Rare-Event Structural Failure Probability
15. Minkowski dimension and content of complex continued fractions
16. Exploiting Load/Store Leakage of Sparse Vectors for Key Recovery in HQC

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-21/

1. Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions
2. A Complete classification of the rank of a certain family of elliptic curves
3. Non-ordinary primes and congruences for weakly holomorphic modular forms of level 2
4. Density of Unicritical Polynomials over Local Fields with Rational Periodic Points
5. Arithmetic properties of the 2-color overpartition function $\overline{p}_\ell(n)$
6. Solutions to Two Problems of S\'ark\"ozy and S\'os on Additive Representation Functions
7. Counterexamples of Friedlander--Iwaniec dual sums conjecture
8. An explicit uniform cubic wedge for consecutive Toeplitz minors of the Riemann xi coefficients
9. Twisted Siegel-Weil formulas for $\mathrm{GL}_2$ over non-Galois quartic CM fields
10. A Modular Form Proof of the Irrationality of $\zeta\left(3\right)$
11. On the average number of subgroups of the group ${\Bbb Z}_{n_1}\times {\Bbb Z}_{n_2}$
12. A survey on moments of a class of error terms
13. Consecutive non-square non-primitive tuples in finite fields
14. Torsion of rational elliptic curves over $\Z_p$-extensions of quadratic fields for $p\geq5$, with a slope analysis for $p=3$
15. On Erdos-Falconer distance problem in even dimensions
16. Galois-invariant N\'eron--Severi ranks of Fermat surfaces over number fields: a Galois module, closed forms, a threshold, and exact tables
17. Quadratic residue patterns of length 4 and 5
18. Diophantine analysis and the Braid group ${\bf B}_3$
19. On some sums involving small arithmetic functions
20. Betti-Whittaker periods under duality: variations and applications
21. Jacob's ladders and new $\zeta$-functionals and corresponding $\zeta$-equivalents of the Fermat-Wiles theory based on sums of elementary $\zeta$-pulses
22. Bounded trajectories of quasi-rays on homogeneous spaces and Diophantine approximation with weight functions
23. A short survey the game Bulgarian solitaire and related games
24. A positive answer to the Owings's sumsets question
25. Space of norms on locally algebraic representations
26. Counting subsets of integers free of arithmetic configurations
27. Quantitative Oppenheim in signature $(2,2)$ via determinant values
28. Determinant values on lattices
29. Fricke's trace identity and spin groups

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-20/

1. A counterexample to a conjecture of Thakur on Carlitz-Wieferich primes
2. The Second Term for Strongly 2-Primitive Sets
3. A weighted entropy approach for the quadratic inverse large sieve conjecture
4. Finiteness of the Tate-Shafarevich group over function fields for groups of multiplicative type
5. Sets of unit fractions without two members whose average is a unit fraction
6. Indecomposable translates and degree-$d$ points
7. On the existence of Newman and Littlewood multiples for certain integer polynomials
8. Improved bounds for multiplicative functions in almost all short intervals
9. Arithmetic unlikely intersections in powers of the multiplicative group
10. A comment on the number of $k$-th powers inside arithmetic progressions
11. Upper bounds for moments of analytic ranks of elliptic curves over number fields
12. An improvement on the largest prime factors of consecutive integers
13. Equidistribution for abelian extensions of global fields
14. Defining reduction types of curves via minimal regular and minimal normal crossings models
15. Conjectural Decidability of the Skolem Problem
16. Singular points for cone actions on the product of certain homogeneous spaces

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-17/

1. Beyond the Riemann Hypothesis bounds: A pair-correlation approach to the least prime in arithmetic progression and the smallest quadratic non-residue
2. The Spine: A Supersingular Highway
3. The First Moment of Dirichlet L-functions over Generators of the Character Group
4. Minimal degree of an isogeny between a supersingular elliptic curve and its conjugate
5. Multiple Clausen values and deformed Ap\'ery-like series
6. Equidistribution and the torsor method
7. On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions
8. Double $L$-values of Negative Weight Admitting Series Representations
9. On a character-twisted analogue of Sch\"{a}ffer's equation
10. A Bombieri-Vinogradov theorem for exponential sums over products of k primes
11. Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture
12. Aperiodic tile sets from Sturmian lattices
13. Several families of incommensurable noncompact hyperbolic Coxeter polytopes
14. Aperiodicity and subword complexity in the binary expansion of powers of three
15. Asymptotic Brill-Noether Existence at the Half-Canonical Degree: Energy Pairing, Cheeger Inequality and Covering Radii

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-16/

1. A minimal modularity lifting theorem for Siegel modular forms
2. Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks
3. On the Second Moment of $ L (1/2, \mathrm{As}(f) \times \phi)$
4. Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm
5. On the Second Moment of $L (1/2, \mathrm{As} (f))$
6. Torsion groups of rational elliptic curves over $\mathbb{Z}_p$-extensions of quadratic fields: the $p\le 5$ case
7. Spectral fourth moments of Hecke--Maa{\ss} cusp forms
8. Bernoulli determinants and cuspidal subgroups
9. Generalization of Ramanujan's Continued Fractions for Even Order
10. Representability of systems of proportionally modular numerical semigroups
11. Area correlations related to lattice points in discs
12. The mean value of the digits of $1/p$
13. Exact classification of elliptic curves $y^{2}=x^{3}-pqx$ with rank $0$ and trivial $\Sha[2]$
14. Strongly complete sets and a conjecture of Erd\H{o}s
15. An asymptotic Sidon basis of order $3-\eta$
16. Heat Kernel and Closed Geodesic Asymptotics for Nilpotent Coverings
17. Resurgent Lambert series from Feynman and beyond

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-15/

1. A few remarks on the Baez-Duarte Criterion
2. Solomon zeta functions over arithmetic orders
3. Curious identities involving Legendre polynomials and Ap\'ery-like numbers
4. Odd Parts of Derivative Period Polynomials and a Logarithmic Transition Scale
5. Local statistics and average rank of genus $g$ hyperelliptic curves with a Weierstrass point
6. On lower bounds for canonical heights of the map $\phi(X,Y)=(Y,X+Y^D+b)$
7. Euler systems and the symmetric square of a Hida family
8. Cyclic Projective Orbits on Rational Normal Curves and MDS Codes
9. A Note on Iterated Beatty Sequences
10. Ranks of Elliptic Curves Twisted by Quadratic Forms
11. $p$-adic Sum-Product, Projections, and Furstenberg Sets
12. Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation
13. A universal leading-residue formula for Witten zeta functions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-14/

1. A counterexample to a subadditivity conjecture of Cohen for Sophie Germain cyclic numbers
2. Affine monodromy and exact value distributions over finite fields
3. Hyperbolic Arcsine Kernels, Finite Fourier Filters, and Quartic Central Binomial Harmonic Sums
4. Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence
5. Simultaneous popular polynomial differences over finite fields
6. On the Summatory Function of $d_3(n)$
7. Local monodromy of unit root F-isocrystals from Shimura varieties
8. A resolution of Kellner's conjectures on Wilson quotients
9. On a Class of Hypergeometric Sums via Recurrences and Product Binomial-Harmonic Identities
10. Class Number Relations in Abelian Extensions of Global Fields
11. Long Intervals Without Distinct Multiples of the First $n$ Positive Integers
12. Orbit Transversality for Abelian Varieties
13. Sign Patterns in a Two Colored Partition Companion series
14. The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers
15. Greenberg's $\mu=0$ conjecture for lisse sheaves over global function fields
16. The rank of the modular multiplication matrix
17. Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution
18. Sums of Kloosterman sums formed with modular symbols
19. Kloosterman sign changes with moduli having at most five prime factors
20. Positivity and tails of Jacobi theta series
21. Lattice point counting in Cygan--Kor\'anyi balls on Heisenberg groups
22. Disproofs of two conjectures concerning nondeficient numbers
23. Exact Frequencies of Consecutive Quadratic Residue and Nonresidue Patterns Modulo a Prime
24. Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products
25. On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II
26. Unexpected primes of good reduction in quotients of modular and Shimura curves
27. p-adic Properties of Translated Division Polynomials and Somos Sequences
28. Two local zero-sum problems
29. Superlinear complexity of the $(3/2)^n$ steering word
30. Local-global compatibility of automorphic Galois representations over CM fields at $p$
31. Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations
32. A decomposition of Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems
33. The Ramanujan Challenge For AI
34. On the Canonical Height Gap for Polynomial Maps and Portraits of Preperiodic Points of Polynomials with Height $0$
35. Bump-Friedberg type periods beyond the cuspidal spectrum
36. Combinatorial identities derived from explicit formulas of Gauss hypergeometric functions
37. The Aubert and Bernstein involutions for disconnected groups
38. The Arithmetic of Semirings Part I: Ideals
39. Zero-one laws for uniform approximation via Gaussian and Eisenstein integers
40. A dual linear programming bound for sphere packing in dimension 36
41. Intrinsic ergodicity for $\mathfrak{B}$-free integers in number fields
42. The combinatorics of sector renormalization
43. Arithmetic Properties for $k$-Color Analogue of Simultaneously $s$-Regular and $t$-Distinct Partitions
44. Fractal uncertainty principle over $\mathbb{Q}_p$
45. Submultiplicative Polynomials in Combinatorics
46. Exact Cardinality And Nonredundant Parametrization Of Character-Polynomial Codes

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-13/

1. Joint level-weight murmurations for holomorphic newforms
2. Moments of the number of representations as sums of two prime squares
3. Remarks on a theorem of Silverman
4. The complete cubic Walsh spectrum of a permutation-inverse Boolean family
5. First Moment of derivatives of $L$-functions in a nonlinear family
6. Extension of the Equation $\sum\limits_{j=1}^{k}jF_{j}^{p}=F_{n}^{q}$ to a Family of Lucas Sequences
7. Averages of diagonal Elliott-Halberstam problem twisted by M\"obius function with Sobolev and H\"older-Zygmund weights
8. The Young Tableaux Hopf algebra and multiple Schur series
9. Asymptotic Formula for Multipartitions
10. Chevalley-Herbrand formulas and Z p -extensions of a p-principal imaginary quadratic field
11. Hankel determinants of weighted binary sums of digits
12. Counting odd genus $2$ curves with a marked rational $3$-torsion point
13. Explicit height bounds for G-functions and unlikely intersections with lines in tori

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-10/

1. Infinite families of Diophantine quadruples in $\mathbb{Z}[\sqrt{-2}]$ in the remaining exceptional congruence classes
2. Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg
3. Elliptic curves, Fourier ratio, and sampling complexity
4. On an inhomogeneous uniform Littlewood type problem
5. $L^{\infty}$-norm bounds for Siegel--Jacobi cusp forms
6. On a parametric congruence concerning generalized central trinomial coefficients
7. Explicit estimates of the weighted sum $S(x)=\sum_{n \leq x} (-2)^{\Omega(n)} \log\bigl(\frac{x}{n}\bigr).$
8. Explicit upper and lower bounds on certain functions related to $\zeta(s)$ for $s>1$
9. Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions
10. Rademacher-type formula and higher order Tur\'{a}n inequalities for $\ell$-regular overpartitions
11. Modular Nahm Sums for the Inverse Cartan Matrix of Type $D_r$
12. Reduction modulo p of crystalline Galois representations via {\mu}_p-equivariance
13. A Matrix Analogue of Rational Number Systems
14. Waring Problem for matrices over finite local rings
15. Modular Constructions of g-Golomb Rulers
16. Functional Limit Theorems for Random Least Common Multiples
17. Dilated Hankel determinants
18. High-degree cohomology of congruence subgroups of $\text{SL}_n(\mathcal{O})$ via cohomology of $S$-arithmetic groups
19. Sandpile groups of random bipartite graphs and families of distributions with the same moments

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-09/

1. A problem of D. H. Lehmer in short intervals. II
2. Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
3. Four squares from three real polynomials
4. Normal numbers in sparse Cantor sets
5. Schwarz maps for modular curves
6. $p$-adic Hahn series with sparse support
7. Mordell Curves with Ordinates in Arithmetic Progression
8. Global geometrization of local smooth integral models in the Hitchin fibration for $\mathrm{GL}_n$: The Bass case
9. Ideal class monoids of cubic orders
10. Analytic proofs of Andrews-Bachraoui identities related to two-color partitions with evens in one color
11. A proof of Andrews-El Bachraoui's conjecture on the parity of coefficients of a $q$-series
12. Some Comments on Regular Overpartitions modulo $2^k$
13. Extending Recent Arithmetic Properties of Overcubic Partition Tuples
14. On capitulations of even $K$-groups and pseudo-null submodules in $\mathbb{Z}_p^d$-extensions
15. On dynamical irreducible set of polynomials
16. $p$-adic Maass--Shimura operators on $\mu$-ordinary Igusa varieties
17. A higher Gross-Zagier type formula for moduli of shtukas at deeper level
18. Reduction Types of Genus 2 Curves
19. Practical Computations of the Mertens Function: $M(10^{24})$ and $M(10^{25})$
20. A curious congruence modulo primes
21. The $abc$ Conjecture Revisited
22. A problem of D. H. Lehmer in short intervals. I
23. Covers of Bruhat-Tits trees
24. Universality for cokernels of partially random integral matrices
25. Multiplication Beyond Groups: Stratified Fourier Mechanisms in Transformer Circuits
26. Small Matrices with Large Inverses: Unimodular $4 \times 4$ Cases

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-08/

1. A weaker but simpler sieve inequality
2. Integer values of $\tan(\arctan 1+\arctan 2+\cdots+\arctan n)$ are rare
3. An Explicit Expression for MZVs in Terms of Symmetric MZVs
4. Large Sets of Integers with No Harmonic Triples
5. Correlations of zeros of a family of $L$-functions in function fields with symplectic symmetry
6. Small sums of roots of unity
7. An improved upper bound on the Ruzsa number
8. On exotic Diophantine triples in $\mathbb{R}[X]$
9. Steady-State and Transient Heat Conduction Analysis Using a Polygonal Cell-Based Smoothed Finite Element Method
10. The Siegel-Weil formula in geometry and arithmetic
11. Random Multiplicative Functions and Making Squares from Polynomial Values
12. A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions
13. A refined Malle conjecture for Heisenberg groups
14. A Variation Norm Carleson Theorem Along the Primes
15. Degenerations of flat connections on Riemann surfaces
16. The Euler Ensemble as a Turbulent Attractor: Parity Sectors, Zero Modes, and a Zeta Edge
17. Generalisation of Baker's Forcing Method to Arbitrary Prime and NP-hardness of Several $p$-adic Optimisations
18. Closed geodesics in homology classes on random hyperbolic surfaces of large genus
19. A generalised cross-ratio and limits of local heights

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-07/

1. Recovering Kodaira types from $\ell$-torsion on elliptic curves
2. $(a,a)$-Carmichael numbers and greatest common divisors of $p-a$
3. $p$-adic rigidity for $\mathrm{GSp}_4$
4. A finite Guinand-Weil dictionary and archimedean tail order for the truncated Weil quadratic form
5. A Mackey criterion for locally analytic representations
6. Beyond Endoscopy for $\mathrm{GL}_3(\mathbb{Q})$: Functional equation for the $L$-function of a cubic order
7. Refined Humbert invariants and subvarieties of $\Ac_2(\C)$: the rank 3 case
8. Lubin's conjecture for height-one $p$-adic dynamical systems
9. On S\'ark\"ozy-S\'{o}s Theorem related to representation functions
10. Derivative-Free Richelot Isogenies via Subresultants with Algebraic Certification
11. Calculating the floor of y**(1/m)
12. Ramanujan-type identities for alternating Hurwitz zeta functions
13. The discrete logarithm problem in cokernels of $\mathcal{O}_K$-matrices
14. On the inverses of permutation polynomials of the form $h(\psi(x))\varphi(x)+g(\psi(x))$ over finite fields
15. The compositional inverses of the permutation polynomials of the form $x+\gamma\operatorname{Tr}_{q}^{q^n}(H(x))$ over $\mathbb{F}_{q^n}$
16. Extreme values of the real part of the Riemann zeta function
17. A Romanoff-type theorem for $P_2$+{$a^a$: a$\ge$ 1}
18. Modular elliptic curves and hyperbolic uniformization
19. Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon: the first step, the 641-gon
20. Anomalous Partial Quotients in the Continued Fraction of $\sqrt{\zeta(3)-S_N}$
21. Extreme values of derivatives of Dirichlet $L$-functions
22. $p$-adic multiple $L$-functions and twisted multiple Bernoulli numbers
23. A Stretched-Exponential Bound for an Erdos--Graham Unit-Fraction Problem
24. Distinctness of the generalized $n$-dimensional Kloosterman sums
25. On the number of perfect positive definite quadratic forms
26. Improving on the Brun-Titchmarsh Theorem
27. A Gaussian-Perron Smoothed Prime-Side Defect for Local Profiles Near Critical-Line Zeros of the Riemann Zeta Function
28. A proof of Riemann's hypothesis via Hadamard-Weierstrass factorization
29. Complete Asymptotic Expansion of the Additive Mertens Sum $S_k(x)$
30. Symmetric Spectral Reciprocity for $\mathrm{GL}(2)$ and Uniform Subconvexity
31. Supercongruences Arising from Truncated Appell Series
32. A decades-long breakthrough in zero-density estimates and primes in short intervals
33. Pythagorean triples in level sets of completely multiplicative functions
34. On the exterior square $\varepsilon$-factors of $GL_n$
35. Truncated Multiple Zeta Values
36. Class-Number-One Cubic Fricke Companions on $\Gamma_0(2)^+$ and an Exact Chudnovsky Bridge
37. Exceptional rational functions of degree 5 over finite fields: classification by monodromy, ramification, and the Riemann-Hurwitz formula
38. Thue equations that simultaneously fail the Hasse principle
39. Sharp Circular Sampling and Derivative Period Polynomials
40. Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis
41. Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves
42. An improved lower bound for odd integers not of the form $p+2^a+2^b$
43. Large $B_2[g]$ subsets of the first squares
44. Signed graphs with fixed smallest eigenvalue at least $-3$ and their lattices
45. Partitions with parity restrictions: a bijective approach
46. Dynamics of integer zeroes of homogeneous quadratic equations over $\mathbb{R}^3$
47. A Combinatorial Proof for Partitions of Pythagorean Triples Into Three Parts
48. Presenting restricted Steinberg modules of general linear groups
49. A MacMahon Analysis View of 4 Diagonal DSPPs
50. A sharp lower bound for some reciprocal Rado numbers
51. Sharpening Borel's result in Diophantine approximation
52. Theta correspondence as a C*-correspondence
53. Integer Coefficient Power Series with Prescribed Zero Sets
54. The Minkowski grid has robustly many repeated distances

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-03/

1. Utilizing Smoothing Techniques to Bound $|\zeta(1+it)|$
2. Necessary and sufficient conditions on the order of a finite field $\mathbb{F}_q$ for the easy identification of primitive polynomials of degree 2
3. Formalized $q$-series: The Rogers-Ramanujan Identities and Beyond
4. A Pfaffian Proof and Generalization of a Conjecture of Sun Zhiwei
5. On Euclidean systems of ray classes
6. A Coordinate System for Collatz Dynamics
7. Gross-Zagier formula for the $4, 7$ cases of Sylvester's conjecture
8. On a Smoothed Walfisz Divisor Problem
9. The Eichler--Selberg trace formula for Hilbert cusp forms, the class numbers of quartic CM fields, and their distributions
10. Genuine and strongly genuine polynomials: With an application to the persistence of Galois groups under specialization
11. Iwasawa-Type Spectral Resultant Growth Laws for Grover Walks on Graph Towers
12. Algorithms for hyperelliptic Mumford Curves $p$-adic Uniformization, $p$-adic integrals and $p$-adic heights
13. The trianguline variety for reductive groups
14. Cyclic Codes and Cyclically Covering Subspaces over Finite Fields
15. Beyond the Giampietro--Darmon Conjecture
16. The Gauss periods and cyclotomic matrices involving Gauss sums over cyclic groups
17. A note on polyhedral cones and toric polylogarithms
18. The universal zero-sum invariant and weighted zero-sum for infinite abelian groups II
19. Recent progress on the geometric Bombieri--Lang conjecture
20. Black Holes and Random Variables

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-02/

1. Finiteness for \'{E}tale Fundamental Groups of N\'{e}ron Models
2. Critical Zeros and Unconditional Mean Value Theorems for twisted $\hbox{PGL}(2)$ and $\hbox{PGL}(3)$ $\mathrm{L}$-functions
3. Functional Equations Characterize Dirichlet Characters
4. Character sums over smooth numbers
5. Depth Two Mock Modularity by Eisenstein Series Coupling
6. Rank of P\'olya Groups in Lecacheux Parametric Family of Quintic Fields
7. The Minimal Absolute Value of Sums of Fifth Roots of Unity
8. Reductions Of Crystalline Representations Of Fractional Slope $
9. Distribution of Selmer ranks in prime cyclic extensions
10. An absolute bound for generalized Diophantine tuples over polynomial rings
11. Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights
12. On a conjecture of Andrews and almost alternating sign patterns
13. Central isogenies and conjugacy classes in reductive groups
14. On the Extended 1-2-3 Conjecture of Pilz
15. $A_3$-formality for pro-2 Demushkin groups
16. Sheared Witt Vectors

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-07-01/

1. Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups
2. On the exponential Diophantine equation $(a^n+1)(b^n+1)=x^2$
3. Several classes of permutation pentanomials
4. Some new congruences and identities for $SOME(n)$, $DSOME(n)$, $\overline{SOME}(n)$ functions and analogues
5. On the Finiteness of Geometric Representations for Varieties over Finite Fields
6. Counting zeros of Artin $L$-functions
7. The classification of real quadratic fields which satisfy Hammarhjelm's condition
8. A cohomological translation of the Kaplansky radical for profinite groups
9. Sign Laws and Mock Theta Functions
10. Diophantine rank stability and non-vanishing of $L$-functions
11. Tamagawa ratios and unbounded Selmer moments
12. Supersingular elliptic curves and twisting endomorphisms
13. Local-global compatibility at $p\neq\ell$ for torsion automorphic forms
14. An Efficient Algorithm for Estimating Prime Counts
15. Construction of Generically Ordinary Families of Hyperelliptic Curves
16. Galois Extensions via Finiteness of Orbits
17. EKOR and BT stratifications for basic unramified $\mathrm{GU}(1,n-1)$ Rapoport-Zink spaces
18. Linear equations and chromatic thresholds in $B_h$ sets
19. A generalization of partition identities of G\"ollnitz-Gordon, Rogers-Ramanujan and Nandi

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-30/

1. Classification of Boolean Cubic Forms in Ten Variables
2. On Brocard's problem with Padovan and Perrin numbers
3. Riesz Means of Quadratic Class Numbers
4. To be or not to be local
5. On Carmichael numbers of the form $2^np^m+1$
6. On the Monotonicity of Higher-Fold Representation Functions
7. Maximal Gaps for Dilated Lacunary Integer Sequences
8. An Explicit Cubic Ramanujan--Sato Series for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$
9. Moment Estimates and Discrepancy for Sums of Square Roots Modulo One
10. Point counts of abelian varieties over finite fields determining their zeta function
11. Distribution of random multiplicative functions in short intervals, with proper normalization
12. On Dense Orbit Transversality for Endomorphisms of Abelian Varieties
13. A Resolution of Erd\H{o}s Problem 731 under Dyadic Regularity
14. Gap-Sums via Quasi-Arithmetic Means with Applications to Fibonacci and Lucas Sequences
15. The van der Corput property for sums of two squares
16. Procounting measures and the Bateman--Horn conjecture
17. A finiteness theorem for mod $p$ Galois representations over global function fields
18. Quantum models of the Riemann zeta function, lattice spin models and algebraic models of entanglement
19. Iterated extensions and the ramification dichotomy
20. For which real quadratic fields is Kim's octonary form universal?
21. Andr\'{e}'s theorem and weakly bounded height
22. The Categorical Local Langlands Correspondence and Anabelomorphy
23. Multiplicative functions additive on partitions of $2k$ nonzero squares
24. Finite-core Volterra reductions for a Weyl-positive Riemann phase kernel
25. On the level of distribution of Goldbach primes and its applications
26. Linear equations on $t$-modules
27. Double weighted sum involving $\mathrm{GL}(2)$ Fourier coefficients
28. Bessel Distributions and Kloosterman Sums
29. Mean values and variances of the digits of $1/p$
30. Harder's conjecture and Hermitian automorphic forms
31. On the diffraction spectrum of the set of visible points in lattices and certain cut-and-project sets
32. On integers of the form \(p+F_{2^k}+F_q\)
33. Structured Solutions of Prime-Base Binomial Congruences
34. Pseudodifferential Jacobi forms and Geometric Rankin-Cohen Brackets
35. Computing sieve integrals using LattE, and the density of integers with a localized divisor
36. Exact approximation order of real numbers in Cantor series expansions
37. Products of prime ideals in ray class groups
38. Moments and sign changes of symmetric power $L$-function coefficients over sums of squares
39. Shifted convolution sums of coefficients of symmetric power $L$-functions with $k$-full kernels over sums of squares in arithmetic progressions
40. Weakly Consecutive Sequences
41. Some quadratically closed fields of nimbers
42. The Thickness of Infinite Sidon Sets
43. A sharp 5/8 bound for an Erd\H{o}s-S\'os pairwise-sums problem
44. Palindromes on the $\tau$-circle: A note for Palindrome Tau Day, 6/28/26
45. Small complete 3-term progression free sets in cyclic groups and vector spaces
46. On a two-color partition series and its companions
47. From some Pisot numerations to topological groups

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-29/

1. Sharp Bounds for Moments of the Dedekind Zeta Function
2. Cohomological Obstructions for Varieties over $p$-adic Function Fields
3. Separable integer partition classes and Slater's list -- II
4. On Franke's theorem in the simplest case
5. Large common values of generalized Ankeny-Brauer-Chowla recurrences
6. Sign law for Ramanujan's third order mock theta function $\rho(q)$
7. Transversal Difference Numbers in Finite Abelian Quotients
8. The Natural Extension for the Triangle Map (a Multi-dimensional Continued Fraction) with An Internal Symmetry from Young Conjugation
9. Perfect powers in sequences of polygonal numbers
10. Kontsevich graphs associated with specific multiple zeta values
11. Series involving parametric harmonic zeta function
12. Average divisibility in character tables of $\mathrm{GL}_2(\mathbb{F}_q)$
13. Stability of the exterior cube $\gamma$-factors for $\mathrm{GL}(6)$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-26/

1. Optimal homological vanishing: cancellation of character sums and Patterson's conjecture over $\mathbb{F}_q[t]$
2. Rank-Two Drinfeld Module over Elliptic Curves
3. Computating decomposition groups and inertia groups using Newton polygons
4. Deterministic and Efficient Ideal Arithmetic via Two-Element Representations
5. Averaged Fourier Estimates and Dyadic Approximation on the Cantor set
6. Adelic Line Bundles, Arithmetic Positivity and Diophantine Geometry
7. Quantitativity in the Mordell Conjecture
8. Determining Newforms via various relations among Fourier Coefficients
9. The Bogomolov Property through Galois Representations
10. A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators
11. Weighted Fruit Diophantine Equations and Hyperelliptic Curves
12. Amplified moments of the Riemann zeta function
13. Sharp endpoint multilinear estimates for oscillatory integrals and spectral clusters
14. Proof of Cigler's conjecture on $q$-Hoggatt numbers
15. On a conjecture by Koll\'ar and Sacc\`a
16. Cusp Excursions, Lattice Points on Manifolds, and the Mizohata-Takeuchi Conjecture
17. Inequalities among higher-order difference sets, or, remarks on a construction of Ruzsa
18. Automorphism Groups of Uniform Dessins d'Enfants of Genus at Least Two
19. On automorphisms of $\mathscr{B}$-admissible and related subshifts
20. Linear Code Conversion in the Merge Regime: General Bounds and Reed--Muller Constructions
21. On the resonant Carleson-Radon transform in all dimensions. The degree one resonant case

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-25/

1. Cusp Volumes and Rational Points on Spheres
2. Binary Trees and Sum of Two Squares
3. Positive dyadic density for rational weighted binary expansions
4. Nonsimilar half-neighbors over fields of characteristic 2
5. Divisibility Biases in the Orders of Elliptic Curve Reductions
6. Negative discrete second moments of Dirichlet $L$-functions
7. Binomial sequences over prime fields
8. Hyperelliptic Atkin-Lehner quotients of Shimura curves
9. Stable Quadratic Polynomials over $\mathbb{Q}(i)$
10. Metric results for dyadic approximation on the middle-third Cantor set
11. Prescribed lifts of 2-dimensional representations
12. Integrality of height-one formal groups
13. Iwasawa Theory for K3 Surfaces over Finite Fields
14. Proof of the Gawron-Miska-Ulas conjecture concerning unboundedness of coefficients of power series expansion of $\prod_{n=0}^{\infty}(1-x^{2^{n}})^m$
15. Number Fields with Arbitrarily Large Minimal Index
16. A resolution of Erd\H{o}s Problem 1061 on the sum-of-divisors function
17. Proofs of four conjectural identities on modular rank four Nahm sums
18. Chebotarev geodesic theorem: split case
19. Every Nonnegative Integer Is a Sum of a Triangular, a Pentagonal, and a Heptagonal Number
20. Potential semistability of Finite height Galois representations: Relative case
21. On $k$-color mex-related partition functions
22. Extensions of maximal symplectic groups acting on the superspecial K3 surface in characteristic $p$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-24/

1. A Local-Global Study of Obstructed Deformation Problems II
2. A Regularised Wallis Hierarchy
3. On Zeckendorf-Niven numbers and arithmetic progressions
4. Elements in $K_4$ and regulator maps of Fermat curves
5. Zeta-regularization and natural boundaries: Sums and products of integers and primes
6. Both $AA$ and $(A+1)(A+1)$ can be small
7. An aperiodic set of Wang tiles for every quadratic irrational
8. A new attack to RSA with small private exponent and partial information
9. The Sylow Divisor Condition: a Resolution of Erd\H{o}s Problem 768
10. Holes in Valid-Extension Sets of Finite Gilbreath Sequences
11. N-ary groups of panmagic permutations from the Post coset theorem
12. The Goncharov Lie coalgebra of a field
13. Tractability versus curse of dimensionality for geometric $L_p$-discrepancies
14. Bialgebraic geometry of B\"ottcher coordinates

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-23/

1. Unbounded Oscillation of Euler-Gompertz Diophantine Errors from Bell and Gould Numbers
2. Differential Addition on Twisted Edwards Curves
3. Differential addition on Jacobi quartic Curves
4. Computing the Greatest Common Divisor of Binomial Coefficients $\binom{mn}{mk}$
5. Duke for Drinfeld
6. On Bounds of Extension Degrees for Similarity of Integral Matrices over Number Fields
7. Congruences for Overcubic Partition $k$-Tuples
8. Isogeny graphs associated to Moret-Bailly families of supersingular abelian surfaces
9. On the modularity of the odd rank generating functions
10. Weighted sum formulas for finite multiple mixed values
11. Geometry of $\mathbf{F}_1$ and Cuntz-Krieger algebras
12. The ratio spectrum of Lagrange constants under linear fractional transformations
13. On finiteness properties of the unramified Iwasawa module of a $\mathbb{Z}_p$-extension with restricted ramification
14. Eichler-Selberg relations for the third-order mock theta functions
15. A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant
16. Level Totients for Integer Mosaics
17. Faster enumeration of primes
18. A Greatest Common Divisor Criterion of Certain Binomial Coefficients
19. A first-exit proof of Cusick's sum-of-digits conjecture
20. The Brocard Problem: Structural Invariants, p-Adic Density, and the Generative Sieve
21. Prime-Power Rarefaction and a Density-One Lower Bound for Erd\H{o}s Problem 400
22. Rank Amplification for Shifted Equal Values of Euler's Totient Function
23. On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\mathrm{GL}_n$
24. Global Extrema of the Zeta Regularized Determinant on Orthogonal Flat Tori
25. Bounded elementary generation of SL_2: nearly the end
26. Panmagic permutations and N-ary groups
27. Ogus's conjecture on F-isocrystals
28. A bilinear approach to the finite field restriction problem, II
29. Bianchi groups and automorphisms of rank-four $K3$ surfaces
30. The natural extension of the $(-\beta)$-transformation
31. Betti-Whittaker periods of the contragredient representations for $\textrm{GL}(n)$
32. Codimensions one and two cohomology of Hecke congruence subgroups
33. How Stark units enter SIC overlaps

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-19/

1. Randomly piercing algebraic sets
2. Consecutive integers free of certain prime factors
3. A note on equidistribution on a product of Shimura curves and Andr\'e--Oort
4. Symmetric square $L$-functions on $\mathrm{GL}_3$
5. Maximal Arboreal Galois Images for Polynomials of Twisted Carlitz Type
6. On the asymptotic density of the ordered pairs $(a,b)$ of positive integers such that $\gcd(ab,a+b)=\gcd(a,b)$
7. Four-digit Kaprekar dynamics in odd bases
8. Generating Function of single-centered Black Hole Index in CHL Models
9. Explicit descriptions of the subfields $(NL)^{pi}$ and $(NL)^{pi}(NL)^{sep}$ of $NL$ and new explicit criteria for $NL = (NL)^{pi}(NL)^{sep}$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-18/

1. On the Diophantine Inequality $\lvert x^{2} - 2^{a}\cdot 3^{b}\rvert < 3\max\{a,b\}$
2. Factorizations of linearized polynomials and extremal curves in odd characteristic
3. Modular Heights of Unitary Shimura Varieties II: Arithmetic Generating Series of Divisors
4. Structured lattices and their applications to security
5. Schneider--Teitelbaum Duality over a Non-spherically Complete Field
6. Explicit constructions for Ramanujan-type congruences
7. Small values of Carmichael's lambda function
8. Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem
9. Generalization of Selberg's $3/16$ theorem for geometrically finite thin subgroups of $\operatorname{SO}(n, 1)$
10. Cram\'er-Type Moderate Deviations for Engel's Series via a Martingale Approach
11. Secretary Problem Thresholds and Convergents of $1/e$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-17/

1. Tail Criteria, No-Go Audits, and Ap\'ery-Type Certificate Obstructions for the Irrationality of e+\pi
2. Arithmetic Properties Satisfied by a Recent Integer Partition Function of Dombos
3. A combinatorial large sieve for Sidon sets, distances, and norm forms
4. Computing Hyperfibonacci Numbers by Means of Matrix Transformations and Jordan Forms
5. Square-Annular Dynamics and Coalescence Frontiers for $n+\tau(n)$
6. An Average-Order Theorem for a Shifted Pairwise-Coprime Extremal Problem
7. Restricted partition functions and additive complements
8. Recursions for Mock Theta Functions
9. On zero-sum problems of two new types
10. Analytic theories around the simplest screw
11. The greedy 3-sumfree sequence $S_{1,g,g+1}$
12. Spectral interpretation of Riemann zeta zeros
13. Spectral Intertwining Operators
14. Single-valued polylogarithms for higher genera
15. Perturbed Polynomial Powers and Bourgain Entropy Obstructions for Khintchin Averages

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-16/

1. Atoms in the Semigroup of Non-Negative Integer Matrices
2. Power and rank-weighted sums in dense finite Sidon sets
3. Rational 2-Cycles for $x^3+bx+a$ and the Elliptic Family $Y^2=X^3+4X^2+16t^2$
4. Every natural number is a sum of distinct semiprime unit fractions
5. On concatenations of two $k$-generalized Pell numbers
6. Counting Algebraic Integers of Bounded Height in Cyclotomic Fields
7. A full $p^{4r}$ supercongruence tower for a level-three symmetric-cube hypergeometric sequence
8. Large values of quadratic Dirichlet $L$-functions of prime-related moduli
9. The Bateman-Horn conjecture on average for generalized von Mangoldt Functions
10. A Beyond Endoscopy Derivation of the Functional Equation for the Symmetric-Square L-Function
11. Square-root cancellation for sums of coefficients of $\operatorname{GL}(m)$-automorphic forms over values of random polynomials
12. A parametric family of primes p = km(m+1) + e + 2kq: heuristic laws, conditional theorems, and unconditional primality certificates
13. On periodic sign changes for weighted representations of integers as colored sums of triangular and generalized pentagonal numbers
14. Thakur's hypotheses on power sums of $\mathbb{F}_q[t]$
15. Indivisibility of ray class groups of real quadratic fields
16. Two $q$-congruences from Jackson's ${}_8\phi_7$ summation and Andrews' ${}_4\phi_3$ summation
17. The difference of the sums of odd and even parts of restricted partitions
18. Obstructions and kernel transport for Hecke lifts of partition q-brackets
19. Divided differences and complex variations of multiple zeta-star values
20. Generalized Bell polynomial operators arising from generalized normal ordering
21. Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields
22. A counterexample to the near-quadratic Elekes--R\'onyai expander conjecture over $\mathbb R$
23. Footnote to a theorem of Phagan on actions of a cyclic group
24. On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons
25. Transformers Learn the Mestre-Nagao Heuristic
26. The distribution of the de Moivre experiment
27. Dominant Zeros of Nekrasov--Okounkov Polynomials
28. Dual Affine Spiral Orbits on $\mathbb{Z}^2$ Generated by Paired Unit Squares
29. Non-Archimedean balanced metrics and their application to totally degenerate abelian varieties
30. Torsors of Generalized del Pezzo Tori and Brauer Groups
31. An Asymmetric Formula for Interval Consonance and its Relation to Harmonic Coincidence
32. The Grothendieck-Katz Conjecture for privileged local systems

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-15/

1. On $U_p$-congruences for meromorphic modular forms with supersingularity
2. Secondary terms for first moments of Selmer groups of twists of elliptic curves over global function fields
3. Residue Restrictions for a Two-Color Partition Series
4. Almost perfect inhomogeneous powers in arithmetic progression
5. Counting the number of $1_{n}$-preperiodic integral points of a discrete dynamical system with applications from arithmetic statistics, VII
6. A Weil Sum Approach to Permutation Polynomials over Quadratic Extensions of Finite Fields
7. Sum of parts in overpartitions and partitions without repeated odd parts
8. Semistable reduction of smooth quartics
9. Explicit local stable resolution of cusps
10. Validated numerics for the Gauss problem on continued fractions
11. Adelic line bundles over a N\'eron model

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-12/

1. Lower bounds on expressions depending on the functions {\boldmath$\varphi(n)$}, {\boldmath$\psi(n)$} and {\boldmath$\sigma(n)$}, III
2. Root Clusters and Multiclusters over Imperfect Hilbertian Fields
3. An AI Proof of 18-Variable Undecidability for Diophantine Equations over $\mathbb Z[i]$
4. Splitting of Polynomial Families via Galois Theory
5. Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants
6. Multi-target hyperbolic sieves and elliptic trace obstructions
7. Ramanujan's and Lim's Identities and Harmonic Maass--Jacobi Forms
8. Discrete Fourier Transform Approach to Cyclically Covering Subspaces of $\mathbb{F}^n_q$
9. Some new modular Nahm sums of ranks 3 and 4
10. Split primes and the Elekes-R\'onyai problem
11. Trace spectra of simplices in large sets
12. Sphere Packings in Higher Dimension (after Boaz Klartag)

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-11/

1. Rankin--Selberg Subconvexity via Spectral Reciprocity
2. Multivariate Period Rings
3. The p-adic Cauchy Theorem and Overconvergent Period Sheaves
4. Proofs of two $q$-congruence conjectures of Guo
5. Modular variants of p-adic fundamental sequence
6. Capparelli's partition theorem as part of an infinite hierarchy: Combinatorial and Weighted Words extensions of recent work
7. A note on a conjecture of Ng
8. Answer to a decomposition question on tori raised by Colliot-Th\'el\`ene and Sansuc
9. Beating Product Constructions for Linear Equations Over Finite Fields
10. On Perfectoidizaiton of Finite Algebras over a Perfectoid Ring
11. Moduli of Supersingular Abelian Varieties in Dimensions $g\leq 5$

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-10/

1. On partial T-adic exponential sums and partial exponential sums with p-power conductor
2. A generic categorical local Langlands correspondence for quasi-split reductive groups
3. A Tsang-range high-moment bound for $\operatorname{Im}\log L(\tfrac12+it,\chi)$ under GRH
4. Prime Quadruplets and Jump Conditions on Arithmetic Functions
5. Unique decomposition of orders
6. On the Ekedahl sieve for the singular locus of the discriminant polynomial
7. Hilbert irreducibility for algebraic points
8. Eisenstein-Kronecker classes on Hilbert moduli spaces and a new construction of Katz's $p$-adic measure
9. Linear relations of four conjugates of an algebraic number of degree eight
10. A Divisor Parametrization for the Erd\H{o}s--Straus Conjecture
11. Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
12. Adjacent comparison bounds and extremal sets for Ruzsa numbers
13. A natural e\~ne product construction of the Big Witt ring
14. Maximal Transcendentality of the Double-Scaled PCM
15. Ind-Banach approach to Grothendieck duality in Rigid-analytic geometry
16. On superspecial hyperelliptic curves of Rosenhain forms
17. The convergent stack
18. On the rank of hypergeometric sheaves on higher dimensional tori

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-09/

1. Arithmetic Symmetry in Ideal Prouhet-Tarry-Escott Solutions
2. Explicit bounds for Dickman's function
3. Weighted Recursions for the Smallest Parts Function
4. Minkowski shapes of pure number fields
5. On the sequence $\mathrm{gcd}(a^n-1,b^n-1)$
6. Monogenity of Fibonacci polynomials and Lucas polynomials
7. A criterion for weighted uniform distribution along functions from a Hardy field
8. Gcd-closed sets and divisibility among power LCM matrices
9. $P$-adic $L$-functions: $t$-modules and Dirichlet-Goss $L$-series
10. Waring's problem involving D.H. Lehmer numbers
11. Arithmetic exceptionality of generalized Chebyshev polynomials of the second kind
12. Erd\H{o}s Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations
13. Murmurations in the Depth Aspect for Maass and Modular Forms
14. On special perfect polynomials over $\mathbb{F}_2$
15. Uncertainty Principles for the Number Theoretic Transform
16. A convexity proof of Pohst's inequality
17. On the degree-$2$ Siegel theta series of extremal even unimodular lattices of ranks $48$, $72$, $96$, and $120$
18. Extremal Type II lattices of rank $72$ are generated by their second shell
19. Transcendence of simple geodesics on finite modular covers
20. Zeta functions over curves
21. The Dirichlet spectrum with respect to $L_1$ norm is $\left[\frac12,1\right]$
22. Polynomial Corners Over finite Fields
23. Degenerate generalized Stirling operators of the first kind arising from generalized Heisenberg algebra
24. Weil's quadratic form via the screw function
25. Fourier Coefficients of Siegel--Eisenstein Series of Degree $2m$ and Weight $m+1$
26. Insufficiency of the algebraic Brauer--Manin obstruction for homogeneous spaces
27. Abelian surfaces of small conductor from genus 3 double covers
28. Multiple zeta values ending with a fixed string
29. On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials
30. Fine-scale statistics for $\mathbb{Q}^n$
31. Power Integral Bases in Polynomial Compositions
32. A note on large values of Dirichlet $L$-functions for characters of fixed order at $1/2<\sigma\leq 1$
33. On the Vinberg Family of K3 Surfaces
34. Covering $\mathbb{F}_2^n$ with Hamming Balls
35. Birkhoff genericity on affine subspaces in horospheres
36. Digit Mixing under Polynomial Maps
37. Restriction estimates for toral eigenfunctions and lattice points in spherical regions
38. Algebraic Hodge generic points are dense
39. Bertini theorems for Hilbert-Samuel multiplicity over finite fields

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-08/

1. Vanishing Coefficients in Products of Quintuple Products
2. Tamagawa number formula for Jacobians
3. A mod $p$ determinant criterion for Cohen--Lenstra convergence of random $p$-adic matrices with prescribed zero patterns
4. Note on the Equivalence of Costas Polynomials and Orthomorphisms
5. Multi-scale properties of continued fraction sets
6. Connection between the Riemann zeta-function and random matrices via hyperfunctions
7. On the factorizations of integers via division algorithms for polynomials
8. Twisted Moments of Rankin-Selberg $L$-functions in the Prime-Power Level Aspect
9. Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
10. Gaps in Multiplicative Sidon Sets II
11. Erd\H{o}s-Kac theorems for discriminants of number fields
12. On the Absolute Geometry of $\operatorname{Spec}\mathbf{Z}$
13. On periods and Jacobians of Heisenberg curves

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-05/

1. Corrigendum to "Isomorphism classes of Drinfeld modules over finite fields"
2. Theorem $(1+1.9)$ on the Goldbach Conjecture
3. The Case of the Second Smallest Modulus: or why we cannot be arbitrarily careless?
4. Hasse-Weil Zeta Functions Modulo a Prime
5. On explicit Fourier expansions of theta lifts to ${\rm SO}(3,n+1)$ arising from elliptic newforms of level one
6. Exotic and inverted Kloosterman sums over semisimple algebras
7. Drinfeld modules in rank 2 with CM and S-unit j-invariants
8. Arithmetic Wu Formulas and the Generalized Hecke Theorem
9. Recent Progress around Cohen-Lenstra Heuristics
10. An Elementary Analysis of the Prime Partition Function
11. A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
12. On a conjecture on Romanoff type sumsets
13. No three algebraic conjugates of degree sixteen sum to zero
14. Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves
15. Arithmetic Kashiwara Regularity and Orbit Classification for Filtered Strongly Equivariant $\mathcal{D}^{\dagger}$-Modules
16. Higgs bundles on the Fargues-Fontaine curve
17. Two notes on valued fields
18. Decomposition Theorem for Perfectoid Rings along General Ideals
19. Stability of the smooth Casselman-Jacquet functor

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-04/

1. Enumeration of modular forms for $\Gamma_1(N)$
2. Voronoi-Hankel Transforms
3. Weighted Recursions for Hurwitz Class Numbers
4. Digit frequencies and class numbers
5. An Explicit Surjectivity Threshold for Digit Sums of Primes
6. Representations of positive integers by three almost-prime squares
7. Correspondence of discrete series representations of $\mathrm{GSp}_{2n}$ and its inner form
8. Integer points close to a transcendental curve: an algorithmic approach
9. The leading constant in Malle's conjecture
10. Khintchine's Theorem for Symmetric matrices via Flows on the Space of Symplectic Lattices
11. A Note on Jacobians with Prescribed Factors
12. Primitive inhomogeneous approximation for fixed non-singular frequencies
13. Local-global conjugacy questions for affine extensions
14. Stochastically evolving ellipsoids with symmetries

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-03/

1. A Note on Diophantine Approximation with Restricted Denominators
2. A Fibonacci theorem for Collatz trajectories via modular graph structure
3. Generalized polygonal number representations
4. Explicit generators of the space of modular forms
5. On the Schematic and Analytic Constructions of the Local Langlands Category
6. On the Argument of the Lerch, Chowla--Selberg Formula and CM Values of $\eta(\tau)$
7. Diagonal Condition in Multiplication Table of $\displaystyle {\, \mathbb{Z} [i] / (\alpha) }$
8. Planes in quadratic 4-space and associated shapes of lattices
9. Majorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual Codes
10. The Fontaine operator at cusps of modular curves at infinite level
11. Pair correlation of $\alpha n^{\theta}$ for random $\theta$
12. A $q$-Analogue of a Supercongruence Related to Van Hamme's (B.2) Supercongruence
13. Some new results on determinants and permanents
14. A note on partitions in the image of pre$_2$
15. On maximal Dynkin friezes
16. A conjecture of Glasby, Praeger, and Unger on permutations of $S_n$
17. On $\mathbb J$-strata with Parahoric Stabilizers in Affine Deligne-Lusztig Varieties
18. Cassini's identity for k-bonacci numbers
19. An Iwasawa-type asymptotic formula for multiple $\mathbb{Z}_p$-coverings of graphs
20. On the prime field spherical restriction conjecture in four dimensions: breaking the Stein-Tomas exponent and applications
21. Complete Families of Curves in the Moduli Space of Genus g Curves
22. Half of finite abelian groups are unit groups
23. The Abel--Jacobi map over the twistor-$\mathbb{P}^1$ and real local class field theory

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-02/

1. Perfect powers in the product of denominators of elliptic curves
2. On $\mathbb{Z}_2$-extensions of real quadratic fields
3. Prescribed realisation of longest runs in continued fractions
4. Polylogarithmic Analogues of Euler's Constant
5. On the $P(t)$-adic Littlewood conjecture in odd characteristics
6. Locating a shortest vector in certain $2$-dimensional lattices
7. On indecomposable elements in lattices
8. The categorical local Langlands conjecture
9. A further study of polynomial $g_{n,q}$ over finite fields
10. Topological and Diophantine properties of lattice subset projections
11. Tame Galois Groups, Linking Numbers and Mildness
12. Piatetski-Shapiro Primes in short intervals
13. Additive Rigidity for Images of Rational Points on Abelian Varieties II: The General Case
14. A Sharp Reverse Minkowski Inequality for the Gaussian Mass of Integral Unimodular Lattices Through Rank $32$
15. Sums of Apostol's M\"{o}bius functions of order $k$
16. Distinguished defining polynomials for extensions of p-adic fields
17. Geometrization of summation formulae for quadrics
18. High moments of random multiplicative functions twisted by Fourier coefficients of modular forms
19. Intrinsic Subgroups and the $\ell$-adic Galois image
20. On a problem on a generalization of Euler's totient function
21. On cyclotomic matrices related to Kloosterman sums over finite fields
22. Infinite Moments of Class Groups for Solvable Fields with a Normal Abelian Subgroup
23. Applications of a formula of Maesaka-Seki-Watanabe type for multiple harmonic $q$-sums
24. Universality of the cokernels of random $p$-adic matrices with inhomogeneously balanced columns
25. On the unit equation $\varepsilon+\delta=n$ in cubic fields
26. On periods of Elliptic curves
27. Arithmetic regularity as an alternative to transference
28. Cyclotomic factors of rational necklace functions
29. Analogues of the Lindel\"of Hypothesis for the Barnes multiple zeta function and related problems
30. Finding the complement of an elliptic curve inside a Jacobian
31. The Primes are $2$-Accessible
32. Infinitely many holes in connectedness loci for collinear affine iterated function systems
33. Non-Archimedean Massera-Schaffer-Maligranda-Pecaric-Rajic Inequality
34. Hitting Arithmetic Progressions at the Square-Root Scale
35. The 1/2-Conjecture for $q$-Binomial Coefficients with Fractional Index
36. Three-color van der Waerden numbers grow super-exponentially

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-06-01/

1. Density of subsets of squarefree elements in certain Dedekind domains
2. On the density of rational lines on diagonal cubic hypersurfaces, II
3. Transcendence and measures via the refined Diophantine exponent
4. An Improvement of Konstantoulas' Density Constant
5. Perfect powers among Jacobsthal numbers
6. Integrality of Averages of Roots of Unity and Perfect Isometries
7. The Bogomolov property for $p$-supercuspidal eigenforms
8. Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve
9. On the asymptotic average diameter of blocks of uniformly distributed sequences and related results
10. Moments of partition statistics, Bell polynomials and Eisenstein-type series

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-29/

1. On Ramanujan's $q$-Continued Fractions of Order Thirty-Four and Sixty-Eight
2. Asymptotic formulas for sums of elements from a multiplicative group
3. On a conjecture of Goldmakher
4. Mersenne numbers and the doubling map
5. Weierstrass semigroups at totally ramified places of degree one on linearized function fields
6. On the power of the discriminant of a univariate polynomial as a certain determinant in positive characteristic
7. Inducing Whittaker Functions from Higher Ranks
8. The weighted large sieve through Parseval
9. Iwasawa invariants of Bertolini--Darmon Theta Elements
10. Canonical extensions of $p$-adic shtukas on toroidal compactifications of Shimura varieties
11. Bourgain's $L^2$ pointwise ergodic theorem over function fields
12. Subsequence Sums in Permutations
13. Superspecial plane quintics with large automorphism groups
14. Lift-independence problem in the $P$-adic Simpson correspondence for curves
15. A note on Azumaya algebras and one-forms

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-28/

1. Some Remarks on $\tau$-Congruent Numbers
2. Linnik's problem for multiplicative functions
3. $Q$-difference analogue of the Stothers-Mason theorem
4. Good Integers: (T,k)-Subclasses and Applications to Galois Duality in Coding Theory
5. Mixed thresholds in the Lonely Runner Conjecture
6. Transformation Formulae and Applications for Double Lambert Series
7. Additive Diophantine Equations involving S-Units, Factorials and Ternary Recurrences with repeated root
8. Metrical theory of signed Engel expansions
9. A unified proof of conjectures on the spaces of multiple $q$-zeta values
10. On the analytic continuation of the Riemann zeta function
11. Equidistribution of CM points and RM curves
12. The sum-product conjecture is false for real numbers
13. Riemann and the logarithmic derivatives of zeta
14. Proofs of Two Positivity Conjectures of Guo
15. Brauer--Manin obstruction from failure of Kodaira vanishing in positive characteristic

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-27/

1. A note on uniform version of Littlewood inequality and Fibonacci numbers
2. On planar functions over $\mathbb{F}_{q^3}$
3. Problems in additive number theory, VII: The structure of additive $h$-bases for $n$
4. Connected components of the ranges of twisted divisor functions on number fields
5. Notes on congruence zeta functions via a Berkovich approach
6. Towards a generalized Maeda conjecture for modular forms with quadratic nebentypus
7. Saturation and No-Go Theorems for Scalar Poisson Certificates of Gaussian Mass Maximality
8. Lower bounds for the Hausdorff dimension of expressible sets
9. Ultra Kolyvagin systems and higher Fitting ideals of Iwasawa Selmer groups
10. Words for generalized Markov numbers
11. Products involving the real parts of Jacobi sums and related cyclotomic matrices
12. Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties
13. The Northcott Property for Composites of Number Fields of Bounded Degree
14. Inhomogeneous Approximation by Sums of Roots
15. The V/L recursion for Macdonald's 7th Variation Schur polynomials
16. Prime Certificates for Exact Vertex-Coprime Ramsey Numbers
17. Rank-two recurrence results for polynomials and questions of dynamical Mordell--Lang type
18. A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$
19. Structural properties and tilting correspondences of perfectoid towers

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-26/

1. On some arithmetic conditions of recurrent sequences modulo prime p
2. On the Harris-Viehmann conjecture for Hodge-Newton reducible local Shimura data of abelian type
3. On the binary digits of the Erd\H{o}s-Borwein constant
4. The $\theta = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$-functions
5. Counting Rational Points on Danielewski and Double Danielewski Surfaces over Finite Fields
6. Tribonacci properties of identities, matrices, and determinants
7. Valuation Separation for Coprime Lucas Products
8. Equality in a Reverse Minkowski Shell Bound for Integral Lattices via Spherical Designs
9. Simultaneous Periods for Families of Rational Maps Modulo Primes
10. Hilbert-90 quotient maps, torsion defects, and symmetric monodromy
11. Lubin-Tate representations over nontrivial finite Galois extensions of $\mathbb{Q}_{p}$ are not Aut-intrinsically Hodge-Tate
12. Variational estimate for the family of discrete averages associated to simplices
13. The Frobenius problem for shifted square sequences starting with a multiple of 4
14. A Note on Abelian Monogenic Trinomials
15. Incidence Obstructions for Power Products in Elliptic Divisibility Sequences
16. Banded quadratic digit functions along irreducible polynomials over finite fields
17. A proof of the $4,7$ cases of Sylvester's conjecture on cube sums
18. Boundary CM points and class groups of small exponent
19. Orbit decomposition statistics for discrete dynamical systems: the Ces\`aro mean and a large deviation principle
20. On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q+1} = X^n(X^n + 1)$
21. The $\Delta$ property: a bridge between split graphs and Number Theory
22. Lattice point counting problems on step-two nilpotent Lie groups

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-25/

1. The Poisson Tail Conjecture for Primes in Short Intervals
2. Cullen and Woodall numbers in Padovan and Perrin sequences
3. Distributions of Iwasawa $\lambda$-invariants of $\mathbf{Z}_p$-towers over supersingular isogeny graphs
4. On modular forms of rational weight satisfying the canonical second-order linear modular differential equation
5. Congruence Classes of Supporting the Erd\"{o}s-Straus Conjecture I: Tame Solutions
6. Computing Gamma(p/q) with Beta function values
7. Concise and elegant proofs of three formulas for complete Bell polynomials
8. Sets of large values of polynomial multi-correlation functions
9. Definability via the tilting correspondence
10. Top-dimensional rational cohomology of the congruence subgroup $\Gamma_{0,n}^+(p)$
11. Balanced intersection size distributions in projective planes

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-22/

1. On the Natural Density of Monic Integer Polynomials with Roots in a Fixed Number Field
2. Port Fillings for Primary Pseudoperfect Numbers
3. A generalization of the Erd\H{o}s-Sierpi\'nski conjecture
4. A Matrix-Theoretic Exact Formula for Counting Primes in Intervals Between Consecutive Odd Squares
5. 2007: An Arboreal Odyssey: A View of Arboreal Galois Representations and Applications, from Early in the Subject's History
6. Escaping Chaos in Random Multiplicative Functions
7. Rational dynamics of a prime-representing map
8. The reverse Goldbach problem and a refined Zsiflaw--Legeis theorem
9. Coset-refined trace statistics, nodal characters, and affine branches in cubic norm tori
10. A Uniform Random-Lattice Tail Bound for the SVP Kissing-Profile Parameter
11. On the structure of fine Mordell-Weil groups over a $\mathbb{Z}_p$-extension and its intermediate subextensions
12. The distribution of semi-integral points on a class of singular cubic hypersurfaces
13. A quick distributional way to reproduce some results of the Riemann zeta function
14. A Complete Characterization of Heron Triangles with Two Perfect Square Sides and the All-Square Equivalence Condition
15. Arboreal Galois Groups of a PCF Map with Strictly Pre-periodic Critical Points
16. Rethinking the work of Langlands on Eisenstein series
17. Lines in the prime number graph
18. Bell Transforms of Arithmetic Functions: Euler Products, Congruences, and Polynomial Sequences
19. Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$
20. From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems
21. Graphs from quadratic forms and vector spaces over finite fields
22. Closed geodesics in short intervals for random hyperbolic surfaces

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-21/

1. High-Precision Approximation of Riemann Zeros via the Truncated Weil Form
2. Eigenvalue Distribution of $p$-adic Random Matrices Among Algebraic Extensions, with an Analogue for $p$-adic Random Polynomials
3. Bounded-box reductions in the Subbarao-Warren problem for unitary perfect numbers
4. On discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator
5. Limiting Distribution and Rate of Convergence for GL(3) Fourier Coefficients
6. Beyond endoscopy for $\mathsf{GL}_2$ over $\mathbb{Q}$ with ramification 4: contribution of non-elliptic parts
7. Generalized Fermat equation over cyclotomic $\mathbb{Z}_l$-extensions of totally real fields
8. Precise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci Lattices
9. A Local Valuation Criterion for Quadratic-Permutation Interleaved Zadoff--Chu Sequences
10. Quasiautomorphic forms are isomorphic to vector-valued automorphic forms
11. On a conjecture of Amdeberhan, Andrews and Ballantine for double Lambert series
12. Binomial coefficients with divisors avoiding an interval
13. An Improved Upper Bound for the Dirichlet Spectrum in Diophantine Approximation
14. Arithmetic Properties of Overcolored Odd Partitions
15. Sharp omega results for the divisor and circle problems
16. Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness
17. Measuring Decidability as Related to Busy Beaver Numbers
18. Extensionalism without Logicism: Ambrose and Extensional Logic
19. An explicit lower bound for the unit distance problem
20. The pro-\'etale fundamental group of singular schemes
21. Remarks on the disproof of the unit distance conjecture
22. A strange continued fraction associated with the Romik map

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-20/

1. The generalized Montgomery-Hooley formula: A survey
2. Short Salem polynomials
3. Fibonacci Numbers and Vieta Jumping for a Rational Diophantine Equation
4. Hal\'asz theorems for Gaussian ideals in sectors and short intervals
5. On nonconvex constellations among primes II: (458,3240)
6. A formula of counting divisors in integers rings: a generalization of the divisor function $d_0(n)$
7. On optimal $p$-adic uniformization of unitary Shimura curves
8. A Determinant Congruence Conjectured by Sun
9. Sun-type determinant and permanent congruences
10. Two determinant evaluations in Sun's conjectures involving Legendre symbols
11. On the Goldbach problem with restricted primes
12. The inhomogeneous Khintchine Theorem in dimension two
13. Split-prime supercongruence at the mixed CM point (1/6, 1/3; 1)
14. A Fourier-Free Density-Increment Proof of Roth's Theorem
15. Motivic Galois theory for one-loop Feynman integrals in momentum space

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-19/

1. Boundary Value Problems on $p$-Adic Analytic Manifolds
2. Factorization of Additive Polynomials and van der Geer--van der Vlugt curves in characteristic 2
3. Explicit Formulas for the Casimir Eigenvalues of $SL(n,\mathbb{Z})$-Maass Forms
4. One-level densities of large even and odd orthogonal families of automorphic L-functions
5. Gaps of Binary Numerical Semigroups and of Binary Inclusion-Exclusion Polynomials
6. Counterexamples to integer-coefficient criteria for recurrence along functions from a Hardy field
7. A Degree-Two Hilbert--P\'olya Realisation by Causal Riemann-Surface Operators
8. On the finite transcendence of Frobenius traces for abelian varieties over $\mathbb{Q}$
9. Multiplicative independence in the sequence of $k$-generalized Pell numbers
10. Linear independence of periods related to polylogarithms
11. An update on the Linnik--Goldbach and Romanov problems
12. Non-admissibility of some universal supersingular representations
13. A note on the $q$-adic valuation of $\sigma_k(n)$
14. Decay of weighted cusp counts for congruence subgroups of $SL_2$ over number fields
15. On some constancy of Hecke eigensystems for Drinfeld cuspforms of level $\Gamma_1(\mathfrak{n}\wp^r)$
16. On the Periods of Ikeda-Yamana Lift for the Unitary Group I
17. Sum of consecutive powers as a perfect power
18. Classicality of Hilbert modular forms
19. Three Brillhart-Lehmer-Selfridge primality proofs for Wagstaff numbers
20. Covering systems where the prime divisors of all moduli are only $2$, $3$, or $5$
21. Linear equations in Piatetski-Shapiro primes
22. Epstein vector zeta functions related to the ADE Lie algebras
23. n-ary elliptic groups, rings, and primes in arithmetic progressions
24. Module Lattice Security (Part III): Structured CVP Distance on the Log-Unit Lattice
25. Rationality problem for norm one tori of tensor products of \'etale algebras and Hasse norm principle
26. Explicit cost analysis of Toom-4 multiplication for incomplete NTT in lattice-based cryptography
27. Iterative maps emerging from cohomological structure of primes
28. Genus formulas for dormant modular curves and asymptotic behavior of their function fields

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-18/

1. Improvements to Jacobian Arithmetic in Global Function Fields
2. Counting solutions to the quadratic determinant equation
3. Explicitly combing hedgehogs over fields of Stufe 4
4. On the Face Map of the Admissible Set With Iwahori Level
5. Bailey pairs, Eichler integrals and unified Witten-Reshetikhin-Turaev invariants
6. Positive density for Sun's $2^k+m$ conjecture
7. Eisenstein circle packings and the Eisenpint Schmidt arrangement
8. Duality of analytic Hopf algebras and the Amice transform
9. Hecke Eigenvalues of Ikeda Lifts
10. On Drinfeld's representability theorem
11. Extensions of the Furstenberg-S\'ark\"ozy theorem via the arithmetic level-$d$ inequality
12. A Weyl-type theorem for Diophantine approximations driven by LCA groups and applications
13. Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Reduction
14. A new construction of permutation polynomials over $\mathbb{F}_{q^3}$
15. On the number of directions formed by Cartesian products in $\mathbb{F}_{p^2}^2$
16. Evaluation of two determinants involving $q$-integers

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-15/

1. A Generalized Closed Form of Ramanujan-Type Fourier Cosine Transform via Meijer's G-Function
2. Parity vectors and paradoxical sequences in the accelerated Collatz map
3. Local certification of residual squareclasses in $\mathbb Q(\sqrt{2},\sqrt{pq},\sqrt{ps})$: one-bit, affine, and finite-choice Hilbert-symbol frameworks
4. Presentations of Galois groups of unramified extensions of global fields and its predicted distribution
5. Kodaira-Neron statistics for rational elliptic curves with $j$-invariant 0 and 1728
6. How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves
7. L-indistinguishability for covering groups of algebraic tori
8. Fibonomial determinants
9. A density version of quaternary Goldbach problem
10. On Maximal Prime Gaps
11. Patterns on elliptic curves beyond Bremner's conjecture
12. On Vu's restricted box estimate in Waring's problem
13. Solutions for Hecke Sum Questions of Banerjee and Bringmann
14. Real geometric transcendence for the Gamma function
15. Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes
16. McShane-Rivin norm balls and simple-length multiplicities
17. Sophie Germain, math\'ematicienne extraordinaire: A story stranger than fiction
18. The R\'enyi entropy of the order of a random permutation
19. Improved Ramsey bounds for generalized Schur equations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-14/

1. A connection between low-lying zeros and central values of $L$-functions
2. Componentwise height bounds for polynomial value-set lifting
3. Wieferich Primes and Monogenic Trinomials
4. On Galois Embedding Problems Arising from 3-Torsion of Elliptic Curves
5. Large values of shifted mixed character sums
6. Fields where torsion forms decompose
7. Tautological modular forms of level two and degree two
8. Almost Affine Invariance Over Prime Fields: Green Problem 90
9. Nonexistence of certain classes of generalized bent functions: Revisiting the element partition method
10. A note on arithmetic progressions with restricted differences
11. When Does the Dice Sum Become Prime?
12. Graphs of Hecke operators in mixed ramification

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-13/

1. The 2-part of the Bloch-Kato conjecture, and indivisibility results, for $K_2$ of some elliptic curves
2. Two dimensional arithmetic progressions avoiding squares
3. Explicit determination of a class of permutation rational functions in any characteristic
4. Bigness of Canonical Quadratic Points on Curves of Genus 4
5. Weil-Moore anima
6. Squared edge lengths of regular simplices with rational vertices
7. Homological sieve and Manin's conjecture
8. Analytic Properties of Necklace Polynomials
9. Local height arguments toward the dynamical Mordell-Lang conjecture
10. $\ell^{p}$ improving estimates for multilinear forms motivated by distance graphs

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-12/

1. Frequency Ordered Ratio Families Arising from the Factorization of $p_{m-1}+1$
2. A Complete Answer to Erd\H{o}s Problem 690
3. Rational Base Descent: A Deterministic Algorithm for Factoring Structured Semiprimes
4. Some Omega results for Dirichlet $L$-functions
5. Multiple integral representations of the Catalan's constant
6. Non-$R$-trivial proper projective similitudes in type $A_3\equiv D_3$
7. On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of a family of real quadratic fields in which $2$ splits
8. Rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields
9. On the coefficients of the Taylor expansion of $L$-functions of elliptic curves
10. Low-Lying Zeros on the Critical Line for Families of Dirichlet $L$-Functions
11. On the exponent of distribution for convolutions of $\operatorname{GL}(2)$ coefficients to smooth moduli
12. An analogue of a formula of Popov II
13. The variation of zeros of the Miller basis
14. Lacunary recurrences and 2-adic properties of Eisenstein series
15. On Ramanujan Primes for Hecke-Maass Cusp Forms
16. Congruences of first syntomic cohomology groups
17. The Serre Derivatives and Zeros of Modular Forms
18. An explicit Galois descent for multiple $t$-values of maximal height
19. Proof of a conjecture of Andrews and Bachraoui on a Hecke sum
20. Reciprocals of Subsum Polynomials
21. $p$-adic Congruencens of Generalized Euler Numbers and Relations to Even Zeta Value
22. Learning from Ramanujan: Elementary Approaches to Profound Ideas
23. The martingale evolution of probability measures defined via the sum-of-digits functions
24. Invariant measure for double base expansions
25. Refined obstructions to local-global principles for 0-cycles
26. Deterministically finding an element of large order in $\mathbb{Z}_N^*$
27. Convergence of orbital integrals on unitary groups in positive characteristic
28. Poisson approximation of random lattices
29. A solution to a strengthened conjecture of Bukh, van Hintum and Keevash on additive bases

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-11/

1. Three-term arithmetic progressions of consecutive powerful numbers
2. On almost primes solutions to forms of odd degrees in many variables
3. Poissonian correlations of $\alpha n^d$ mod $1$
4. Anderson generating function of rank-one Drinfeld Module over rational function fields
5. A Deterministic Cryptographic Prime Generation Chain over Monogenic Cubic Number Fields and their Generalizations
6. Weighted Distributions of Complex Multiplication Orders in Ordinary Isogeny Classes
7. Remarks on the distribution of Dirichlet $L$-functions along cosets
8. A strengthening of Chang's lemma
9. Multifractal analysis of power means for the Schneider map on $p\mathbb{Z}_p$
10. On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groups
11. Brik's sequence: a strange recursion
12. On ratios of theta functions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-08/

1. A Structure Sheaf for Kirch Topology
2. Multiple modular L-functions and modular iterated integrals
3. Rankin--Selberg coefficients in arithmetic progressions modulo prime powers
4. The quotient problem for linear recurrence sequences
5. Evaluation of eight different families of cubic Euler sums
6. $\delta$-Badly approximable numbers and ubiquitously losing sets
7. A multidimensional Szemer\'{e}di theorem in integers
8. On algebraic twists with composite moduli, II
9. Asymptotic Statistics of Odd Unimodal Sequences: Rank Distributions and Probabilistic Structures
10. Equidistribution of Eigenfunctions of Quantum Cat Maps

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-07/

1. A new perspective on the rank of Mazur's Eisenstein Hecke algebra
2. Special periods and some non-tempered cases of the Gan-Gross-Prasad conjecture
3. Rational orbits under correspondences
4. Thin subbases of Piatetski-Shapiro sequences
5. Fixed-point lifting and ghost periodic points for Chebyshev polynomials modulo odd prime powers
6. A Ceiling Continued Fraction Approach to the Erd\H{o}s-Straus Conjecture: Heuristic finiteness of counterexamples
7. Small values of signed harmonic sums and logarithmic means of multiplicative functions
8. $\mathbb{G}_m$-cohomology of $p$-adic Stein spaces
9. Statistics of the Genus Number of $S_3 \times C_2$ and $D_4$-fields
10. Exponential sums over singular binary quintics
11. Non-Expansive Matrix Based number Systems
12. Multiplicative $f$-ic forms on algebraic varieties arising from Thaine's generalized Jacobi sums
13. The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations
14. The top cohomology of principal congruence subgroups of special linear groups over Euclidean number rings
15. Theta functions and transformations of bilateral basic hypergeometric series
16. Appell function proofs of recent and old mock theta function identities
17. On a polynomial involving quadratic residues modulo primes
18. A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
19. $p$-adic Manifold Learning and Benchmark Tasks from Impartial Games
20. The McKay correspondence and local heights for wild-by-tame split metacyclic groups
21. Energy and Vertex Energy of Modified Divisor Prime Graphs
22. The Erd\H{o}s-P\'osa property for prime-length cycles fails (and beyond)

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-06/

1. Sign changes of the Liouville function in arithmetic progressions
2. Monogenity of pure quintic fields: the power of sieving
3. Behaviour of Certain Crystalline Representations modulo $2$
4. Infinitesimal characters for the completed cohomology of $\mathrm{GL}_n$ over CM fields
5. Lectures on Condensed Mathematics
6. Optimal embeddings for maximal orders of central simple algebras of degree 3 over number fields
7. Joint extreme values of $L$-functions on and off the critical line
8. A multivariate Strassmann theorem
9. Congruence rigidity of algebraic groups
10. Real approximation for homogeneous spaces with finite stabilizers
11. On the largest Sidon subset in a finite subset of $\mathbb{R}^N$
12. Analytic summation of series involving higher-order derivatives of Chebyshev polynomials of the second kind and their applications to convolved linear recurrent sequences
13. Table-Based Encodings for Conway's Doomsday Algorithm: Vectorized Doomsdays and Doomyears
14. Signed sumsets and restricted signed sumsets in groups and fields
15. Characteristic-free approaches around Yu's construction
16. Lectures on Analytic Geometry
17. Small Matrices with Small Inverses: Unimodular Zerofree Cases

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-05/

1. Monogenic Fields from Polynomial Compositions with Applications
2. Sets of integers satisfying Bateman-Horn statistics
3. Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor
4. A logarithmic structure theorem for multiplicative functions with small partial sums
5. 3-class field towers with 2 or 3 stages
6. A note on bilinear sums with modular square roots
7. Archimedean arithmetic Siegel--Weil formula for general weights over Shimura curves
8. Numbers in a Beatty sequence which are orders only of cyclic, abelian or nilpotent groups
9. On the generalized inverse tangent integral and Catalan's constant
10. Gaps in Multiplicative Sidon Sets
11. On the Sum of a Prime and a Number that is not Square-Free
12. Expansion in $\text{SL}_2(\mathbb Z/q\mathbb Z)$ and Zaremba's conjecture
13. Cusp forms and parabolic cohomology classes for symmetric spaces of rank one
14. The generalized Fermat equation $Ax^2 + By^r = Cz^p$ and applications
15. Reductions of $\mathrm{GL}_2(\mathbb Q_{p^f})$-Banach spaces of slopes in $(0,1)$
16. A bibasic double sum extension of a $q$-binomial theorem arising out of subspace enumeration
17. Flat Cohomological Purity for Syntomic Schemes over Valuation Rings
18. On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories
19. Twisting Higgs Modules and Functorial Aspects of the p-adic Simpson Correspondence

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-04/

1. The cardinality of a set containing the pairwise sums of a fixed number of integers
2. Primitive sets and von Mangoldt chains: Erd\H{o}s Problem #1196 and beyond
3. Effective multi-equidistribution for translates of unipotent flows and Central limit theorems in inhomogeneous Diophantine approximation
4. Notes on Algebraic Properties and Non-Standard Analysis of the Ring of Integers Modulo Infinitely Large Primes
5. Exponent-one blockers and a Mordell-Weil construction of Euler bricks
6. The Hurwitz sum-of-squares problem depends on the base field
7. Modular Forms and Numerical Explorations of Rational Approximations to $\zeta(3)$
8. On divisor sums due to Erd\H{o}s and Ramanujan
9. Lang-Trotter phenomena and unlikely intersections
10. A note on Zilber-Pink in $Y(1)^n$
11. Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic points
12. On convex bodies with constant non-central sections
13. Delta characters and crystalline cohomology of abelian schemes
14. On the largest sum-free subset of the lattice cube

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-05-01/

1. An $O_K$-basis for the image of a Lubin-Tate logarithm on $\pi$-regular extensions of $K$
2. Mod p Monodromy of Cyclic Covers of the Projective Line
3. Simple Lie Groups of type An as Galois groups over Q
4. On the difference between perfect powers and integral $S$-units
5. An improved non-linear Roth-type theorem in finite fields
6. A divisor function of Wigert and higher degree forms
7. Frobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive Characteristic
8. A torsion-intersection proof of perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers
9. Asymptotic Vanishing of Stiefel--Whitney Classes for $\mathrm{GL}_n(\mathbb{F}_q)$
10. Polynomial Maps with Constants on Matrix Algebra
11. The proportion of permutations fixing a $k$-set

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-30/

1. Estimating the tail of the singular product in the multivariate Bateman-Horn conjecture
2. Combinatorial sums derived from properties of Legendre polynomials
3. Monsky Matrix and 2-Selmer rank
4. The $p$-powers dividing certain exponential sums
5. Solution to the Erdos problem on distinct residues of factorials
6. Families of Unit Equations and Exponential Diophantine Problems via Integral Points
7. Improved bounds for the Fourier uniformity conjecture
8. Generalized Estermann problem for non-integer powers with almost proportional summands
9. On the automorphisms of the power semigroups of a numerical semigroup
10. Multiplicative convolution and double shuffle relations
11. On Arithmetic Mirror Symmetry for smooth Fano fourfolds

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-29/

1. Elementary anabelian varieties are anabelian
2. Ramanujan, the taxicab problem for polynomials, and the abc-conjecture
3. Linear recurrences and rational Lambert series
4. Trilinear Kloosterman fractions I: partially fixed moduli and unbalanced convolutions
5. Reciprocity and the Maslov Phase
6. Congruences via Partitions with Exactly Two Part Sizes
7. Additive index and Carlitz rank
8. The Divisor Function along a Deterministic Orbit and the Emergence of Ladders
9. The threshold for linear independence of multiple zeta values in positive characteristic
10. Cyclotomic Numbers of Order $q-1$ over $\mathbb{F}_{q^r}$
11. Some results on naive transcendence in the ring of integers modulo infinitely large primes
12. Conditional Upper Bounds for Large Deviations and Moments of the Riemann Zeta Function
13. On numerical semigroups with embedding dimension four
14. A structure theorem for sets with doubling $4+\delta$
15. The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groups
16. A local-global correspondence for perfectoid purity
17. Mild Pro-$p$ Groups and Ordered Monoids

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-28/

1. Lattice point visibility along powers of polynomials
2. On the integrality of modular functions over $\mathbb{Z}[j]$ and Kronecker-type congruences
3. A Proof of Bala's General-$m$ Representation of the Harmonic Numbers
4. Core abaci and Diophantine equations I: fundamental weight
5. Hybrid Conjecture in a Mixed Shimura variety
6. Differences of squares of upper-triangular $2\times 2$ integer matrices
7. On (not) learning the M\"obius function
8. A necessary condition for a congruent number of the form $8k+3$
9. $2$-Selmer groups, $2$-class groups, and congruent numbers
10. The Absolute Anabelian Geometry of Virtual Curves of Arbitrary Genus
11. Picking up the partial sums of the M\"{o}bius function problem with probabilistic number theory
12. Large sieve inequality for sums of Legendre symbols over short intervals
13. Unbounded logarithmic limsup in Erd\H{o}s problem 684
14. On optimization on ravine functions. Minkowski-Cohn moduli surface in Cohn parameterization
15. Non-Vanishing of Cubic Twists of $GL_n(\mathbb{Q})$ $L$-functions
16. On the Gauss circle problem over smooth numbers
17. On D-cap-Modules of Finite Length on Rigid Analytic Spaces
18. Linear Bounds for Differentiable Limits of Weak Pair Correlation Functions
19. On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$
20. Joint Sato-Tate Laws for Transformations of Hecke Eigenvalues: The Vertical Case
21. The asymptotic oscillations of moments related to Dirichlet series with missing digits
22. On the hull of linearized polynomial codes
23. A Milestone in Formalization: The Sphere Packing Problem in Dimension 8
24. A note on The asymptotic uniform distribution of subset sums
25. Eleven, twelve, and thirteen lonely runners
26. Dimension of the motivic Galois group of a 1-motive
27. A Necessary and Sufficient Condition for Uniqueness of Euclidean Division
28. Newman's Tauberian theorem, the Riemann-Lebesgue Lemma, and abstract analytic number theory
29. On classical doubling method gamma factors for certain depth zero representations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-27/

1. A link between error terms when counting smooth and rough numbers
2. The exceptional set for Diophantine inequality with mixed powers of primes
3. Exceptional poles of archimedean Rankin-Selberg L-functions for principal series representations of GL(n,R)
4. On a new modular equation of degree five and Eisenstein series identities of associated levels
5. Higher moments of the symmetric square $L$-function off the critical line
6. Matrices with cyclically monotone rows and Cantor numeration systems
7. Khintchine's theorem for inhomogeneous simultaneous approximation with polynomial decay
8. Asymptotic behaviour of analytic torsion and cohomological torsion for $\mathbb{Q}$-rank $1$ arithmetic groups
9. Non-linear geometry of multiple zeta values
10. Numerical Semigroups with $a_e = 2g+1$
11. A construction method for WZ seeds

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-24/

1. On the reciprocity law in $\mathbb{F}_{q}[t]$
2. Extremal Problems for GCDs and LCMs in Higher Dimensions
3. Relations between higher level Hurwitz class numbers
4. Moments and joint nonvanishing of symplectic $L$-functions
5. Consecutive non-square nom-primitive pairs in as finite field
6. The Smallest Invariant Factor of Elliptic Curves, and Coincidences
7. Galois representations over convergent de Rham period ring
8. Residues of a tropical zeta function for convex domains
9. Spherical Cap $L_2$ Discrepancy -- Blessing of Dimensionality and a Balanced Large-Cap Variant
10. Lusztig constants and endoscopy

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-23/

1. Explicit density computations for certain sets of primes in Lucas sequences
2. On Uniqueness of Mock Theta Functions
3. Minimal $a$-numbers of Artin--Schreier covers of ordinary curves
4. Root numbers for twisted Fermat quotient curves II
5. On the $I(1)$-invariants: Non-abelian Hecke algebra case
6. On the singularities of differential equations satisfied by $E$-functions
7. On the Hyperbolic Fractional Sum of the Divisor Function
8. Non-vanishing of the $p$-adic constant for mock modular forms associated to a newform with real Fourier coefficients
9. On sums of two squares and a basis of order $2$
10. p-adic elliptic polylogarithms and cubic Chabauty
11. Mellin transforms, transfinite diameter and rational approximations of integrals
12. Fractal transference principle for continued fractions of Laurent series

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-22/

1. Optimal Shifting Method in Dirichlet's divisor problem
2. Characterizing monogenic trinomials $\boldsymbol{x^{12}+ax^6+b}$ according to their Galois groups
3. Algebraic numbers and Fourier analysis: Salem's third problem
4. Sums of Hecke eigenvalues along polynomial sequences and base change for $\text{GL}(2)$
5. Classification of Rational Functions of Degree Three over Finite Fields
6. Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations
7. Beyond the square-root barrier: cubic forms of Perazzo type
8. Quartic Rational Diophantine Quadruples and the Euler Surface
9. Division algorithms for norm-Euclidean imaginary quadratic fields
10. Representations of binary quadratic forms by quaternary quadratic forms
11. Pseudometrics and preorders on sets of integer sequences induced by arithmetic functions functions
12. Explicit counting of ideals in number fields of arbitrary degree
13. Global Product Intersection Sets in Semigroups
14. Independent Sets and Continued Fractions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-21/

1. M\"obius disjointness conjecture for Furstenberg's flow on $\mathbb{T}^\omega$ in short intervals
2. Reduction mod $p$ of semi-stable representations of some super-Breuil weights
3. Geometry-of-numbers methods over global fields II: Coregular representations
4. On Regular Higher Power Rational Diophantine Triples
5. Non-liftability of Families of Abelian Varieties with Small $l$-adic Local System
6. The Limiting Distribution of Elliptic Dedekind Sums
7. Supersingular Drinfeld modules, Brandt matrices, and rank-metric codes
8. The sum-product phenomenon for dense subsets of finite fields
9. On the normality of the concatenated Fibonacci constant
10. Markov fractions and Cohn matrices
11. Orderings of Generalized k-Markov Numbers
12. Resolutions of spaces of crystalline representations and modularity
13. Effective Joint Sato-Tate Distribution and Sign Change of Symmetric Power Coefficients
14. A remark on an integral structure of the imperfect coefficient ring of $(\varphi,\Gamma)$-modules
15. Explicit Kodaira-Spencer maps over PEL Shimura varieties
16. Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields
17. Duality Between Prime Factors and The Prime Number Theorem For Arithmetic Progressions -- Higher Order Dualities
18. Sophie Germain Primes and the Totient of Fibonacci Numbers
19. Solvable Descent and the Grunwald Problem for Solvable Groups
20. A Rademacher exact type formula for pod$_2(n)$
21. Families of symplectic Galois representations over small parabolic eigenvarieties for Siegel cuspforms of genus $2$
22. A primality test for $Kp^\ell - 1$ numbers
23. Maximal quadrics over finite fields and minimal codewords of projective Reed-Muller codes
24. Implementing p-adic numbers in Macaulay2 using its foreign function interface and FLINT
25. Markov numbers of semigroups
26. Elementary symmetric polynomials and a potentially injective family of maps on partitions
27. Forbidden subgraphs in divisor graphs and an Erd\H{o}s divisibility problem
28. Superspecial generalized Howe curves of genus 4, 5, and 6 with completely decomposable Jacobians
29. Unirational algebraic groups and tame ramification
30. Near-optimal density theorems for large dilates of large point configurations

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-20/

1. Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
2. Gaussian Behavior and Geometric Gaps in Decompositions from Recurrences with Zero Coefficients
3. Extremal densities for forbidden configurations in $S$-smooth numbers
4. Belyi map verification using certified path tracking
5. Uniform estimates for Delannoy numbers and dimension-free estimates for discrete maximal functions over cross-polytopes
6. On the surjectivity of $(T)$-adic Galois Representations of Drinfeld $A$-Modules of Rank 2 and 3: Density results
7. On a question of Astorg and Boc Thaler
8. Matsuki duality for loop groups
9. Sums of two symbols in $K_2(F)/2K_2(F)$ in characteristic two
10. Adolf Hurwitz and the Fundamental Theorem of Galois Theorie: The K\"onigsberg Lectures of 1890-1891

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-17/

1. The level-8 Apery-limit and a proof of the Ramanujan Machine conjecture Z1
2. Arithmetic functions and learning theory
3. Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory
4. On the Number of Prime Factors of Consecutive Integers
5. Computer vision and converse theorems
6. Another factor of integer polynomials with minimal integrals
7. Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$
8. Counting Theorems for Algebraic Relations
9. Log-Concavity and Infinite Log-Concavity of Linear Recurrent Sequences with Linear Coefficients via Companion Matrix Methods
10. Recurrence Time for Finite Quantum Systems
11. Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$
12. On local integrability results for $p$-adic reductive groups
13. Evaluations of some series via the WZ method
14. Rational analytic syntomic cohomology
15. Borel--Bernstein and Hirst-type Theorems for Nearest-Integer Complex Continued Fractions over Euclidean Imaginary Quadratic Fields

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-16/

1. Representation of Ramanujan's tau function by twisted divisor functions
2. A proof of $p$-adic Gross--Zagier theorem via BDP formula
3. Fourier Dimension in Duffin--Schaeffer Conjecture
4. Distribution modulo one of linear recurrent sequences
5. $p$-adic Linear Regression for Random Sampling with Digitwise Noise

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-15/

1. Simultaneous non-vanishing of Dirichlet L-functions
2. On the $K$-extensions between Serre weights for unramified $\mathrm{GL}_3$
3. The $p$-adic monodromy theorem over algebraic-affinoid algebras
4. Multivariable automatic arrays and transcendence
5. Solubility for families of norm equations coming from abelian number fields
6. Applications of patching the coherent cohomology of modular curves
7. An inverse theorem for sumsets of sets of positive density in the integers
8. On the number of missing integers in partitions

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-14/

1. Order-3 pi-formulas, Apery-like kernels, and Clausen functoriality for Conservative Matrix Fields
2. A comment on the equation $n!!=a_1!!\cdots a_t!!$
3. A formal proof of the Ramanujan--Nagell theorem in Lean 4
4. Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
5. The Number of Solutions to $ax+by+cz=n$ for Fibonacci and Lucas triplets
6. A note on small theta lift
7. Remarks on Brauer-Manin obstruction for Weil restrictions
8. On the Chevalley-Bass number of a field
9. Conjectural decomposition of symmetric powers of automorphic representations for $\mathrm{GL}(n)$
10. Beatty solutions of almost Golomb equations
11. Regular ternary sums of generalized polygonal numbers
12. Local square mean in the hyperbolic circle problem and sums of Sali\'e sums
13. A Fixed-Prime Criterion for Reciprocals in Missing-Digit Sets
14. Branched covers of $\mathbb{P}^1$ and divisibility in class group
15. The solvability of the inverse volcano problem over non-prime finite fields
16. Almost Free Non-Archimedean Banach Spaces and Relation to Large Cardinals
17. Character values and conductors of low-rank groups of Lie type
18. Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24
19. Geometrization of the Schr\"odinger Model for the Minimal Representation of an Even Orthogonal Group: The de Rham Setting
20. Algorithms on the Pyasetskii involution on local Langlands parameters of classical groups
21. Pro-$p$ Iwahori-Hecke modules in semisimple rank one and singularity categories
22. An analogue of irreducible cuspidal representations for the group $PGL(2)$ over a two-dimensional local field

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-13/

1. Galois theory for finite fields
2. Seven squares from three numbers
3. Dedekind zeta functions of non-Galois torsion fields of elliptic curves
4. A Dynamical Lifting Problem For Additive Polynomials
5. Values of algebraic functions at Liouville numbers
6. Identities and transformations for Lambert series and double Lambert series
7. Linear recurrence sequences and palindromic concatenations of two repdigits in base $\beta$
8. Differential operators on locally analytic Shimura varieties
9. Quartic reductions and elliptic obstructions for perfect Euler bricks
10. Bounding the exponential sum on squares of some sifted sequences
11. Modular curves and bad reduction
12. Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$
13. A Neukirch-Uchida Theorem for 3-Manifolds

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-10/

1. On Lower Bounds for sums of Fourier Coefficients of Twist-Inequivalent Newforms
2. Universal sums of generalized polygonal numbers of almost prime length
3. Proofs for Andrews' Conjectures 5 and 6 on $v_1(q)$
4. A Liouville-Type Inequality for Values of Mahler M-Functions
5. Resurgence of high-energy string amplitudes
6. Lifting banal representations of classical groups
7. L-modules are mixed
8. On a descent conjecture of Wittenberg

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-09/

1. On a perturbed Hofstadter $Q$-recursion
2. Order drop, Hecke descent, and a mod $p^4$ supercongruence for symmetric-cube hypergeometric coefficients
3. The Domb Ap'ery-limit and a proof of the Ramanujan Machine conjecture Z2
4. On the Double Lambert Series Conjecture of Andrews-Dixit--Schultz-Yee
5. The Thue-Morse Transform
6. On canonicity for integral models of Shimura varieties with hyperspecial level
7. Reduced Unitary Whitehead Groups over Function Fields of p-adic Curves
8. Boundary Cohomology of Sp6(Z): Trivial Representation
9. A Hal\'{a}sz-type asymptotic formula for logarithmic means and its consequences
10. Arithmetic intersections on non-split Cartan modular curves
11. Random conic bundle surfaces satisfy the Hasse principle
12. Explicit inequalities for the nth lucky number
13. Weighted averages of arithmetic functions and applications to equidistribution
14. On the cohomology of negative Tate twists via cyclotomic descent
15. On a conjecture of Deines
16. $p$-adic Theory for Partial Toric Exponential Sums
17. Congruence modules and Wiles defects of determinantal rings of maximal minors
18. Short proofs in combinatorics, probability and number theory II
19. Topological Indices of Divisor Prime Graphs
20. A note on complex Lie Algebras isomorphic to their conjugate

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-08/

1. Asymptotic distribution of CM points on the reduction of the Drinfeld modular curve
2. On Elliptic Sequences over Commutative Rings
3. A statistical investigation of a divisor-sum function
4. Matchable numbers
5. Proof of a conjecture of Banerjee,Bringmann and Bachraoui on infinite families of congruences
6. There are infinitely many Hilbert cubes of dimension 3 in the set of squares
7. Partial sums of random multiplicative functions with supercritical divisor twists
8. On the computation of base-change lifts and lifts of Hida families
9. Small gaps between consecutive zeros of the Riemann zeta-function
10. On Iwasawa theory of abelian varieties over $\mathbb{Z}_p^2$-extension with applications to Diophantine stability and integally Diophantine extensions
11. Asymptotic expansions of integrals and Nielsen's polylogarithms
12. Theta Cycles of Modular Forms Modulo $p^2$
13. Frobenius nonclassicality of generalized Fermat curves with respect to conics
14. On the largest strongly connected component of randomly oriented divisor graphs
15. Structural Hierarchy of Reid Class of non-Archimedean Banach Spaces
16. Analytically generated sharply o-minimal structures