素数とp進数と格子と多項式とゼータ関数 - 2026/9/23の論文45本

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/2026-09-23/ Infinitely Many Binomial Coefficients of Deficiency One 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 An Integral Representation of the Generalized Fibonacci Numbers Brauer-Kuroda relations for ramified graph covers The Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell Conjecture Moulds, Bimoulds, and some Lie algebras A density version for the sum of nine cubes of primes On the Euler transform and the floor function Distinct exponents in the prime factorization Irreducible polynomials with restricted digits in base $b(T)$ On the generation of multiplicative groups by small primes The density of sums of distinct divisors Density of large holes among power-free lattice points A surprising generalization of the M\"{o}bius function S-integrality for families of ordinary K3 surfaces and algebraicity theorems On the positivity of truncated pentagonal number series and some conjectures of Merca Irrationality Exponents and Partial Quotient Growth in Continued Fractions Abelian $p$-extensions with restricted $p$-ramification and the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q} (\sqrt{q})$ The large sieve through Parseval, Large sifted sets are regular The weighted large sieve through Parseval Large values of the Hurwitz zeta function with rational parameter Equal subset sums and close divisors Boyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_k A certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of Samart Peels of Equilateral Triangulated Surfaces On two families of period integrals related to Catalan's constant Improved rational approximations to Catalan's constant Cokernels of random $p$-adic orthogonal matrices and their linearizations Iterated integrals for generalized Appell functions A divisibility of automorphic periods for the real quadratic base change of $\mathrm{GL}_3$ Stable