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

arXiv math.NTの新着論文12本をご紹介します。

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

arXiv math.NTの新着論文10本をご紹介します。

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

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/2026-05-12/

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

arXiv math.NTの新着論文12本をご紹介します。

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