プレプリどんどん: math.NT

arXiv math.NTの新着論文15本をご紹介します。

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

arXiv math.NTの新着論文19本をご紹介します。

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

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/2026-05-26/

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

arXiv math.NTの新着論文11本をご紹介します。

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

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/2026-05-22/

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

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/2026-05-21/

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

arXiv math.NTの新着論文15本をご紹介します。

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

arXiv math.NTの新着論文28本をご紹介します。

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

arXiv math.NTの新着論文16本をご紹介します。

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

arXiv math.NTの新着論文19本をご紹介します。

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