プレプリどんどん: math.NT

arXiv math.NTの新着論文23本をご紹介します。

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

arXiv math.NTの新着論文29本をご紹介します。

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

arXiv math.NTの新着論文27本をご紹介します。

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

arXiv math.NTの新着論文32本をご紹介します。

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

arXiv math.NTの新着論文48本をご紹介します。

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

arXiv math.NTの新着論文20本をご紹介します。

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

arXiv math.NTの新着論文30本をご紹介します。

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

arXiv math.NTの新着論文22本をご紹介します。

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

arXiv math.NTの新着論文24本をご紹介します。

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

arXiv math.NTの新着論文45本をご紹介します。

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