形式と数体と幾何学的構造 - 2026/10/7の論文31本

arXiv math.NTの新着論文31本をご紹介します。番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-10-07/ Densities of Picard Rank Jumps for K3 Surfaces Over Global Fields CUDA-MPQS: A GPU-Resident Self-Initializing Quadratic Sieve, and the Factorization of RSA-155 On the class number of real multiquadratic fields The One-Power Erd\H{o}s Conjecture for Primes $p \equiv 7 \pmod{36}$ Systems of equations with elements of finitely generated groups and with linear recurrence sequences On eutactic forms Lifting ethereal Bianchi modular forms Gaps theorems for linear forms with cubic coefficients Further results on the paramodular Hecke algebra Primitive normal progressions in finite fields A new bound for the Furstenberg--S\'ark\"ozy theorem using the van der Corput property Carlet's cyclic-additive conjecture for the Kasami monomials A concise proof of the 8 case of Sylvester's conjecture The Artin-Davenport conjecture on cubic forms The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer Perfect powers with few digits and $S$-unit coefficients Primitive Fourier Coefficients of Hermitian Klingen-Eisenstein Series Algebraic Eisenstein classes for $\mathrm{GL}_n$ with applications to the Bianchi case Generating and generalizing MSTD sets through Markov processes On S\'{a}rk\"{o}zy's Local Extrema Conjectures The least prime with a given primitive root and a variant of the larger sieve Local newforms, Pa\v{s}k\={u}nas-Stevens Whittaker functions, and explicit test vectors for $\mathrm{GL}(n)\times \mathrm{GL}(n)$ New integer sequence OEIS A392714 counts Wronskians: fast evaluation via late-growing permutations New algebraic points on covers of elliptic curves Mixing of the BCZ Map Higher additive energies on discrete cubes Block decompositions in the p-adic Langlands correspondence Semisimplicity, purity and Mumford-Tate conjecture for hyper-K\"ahler varieties Special Loci in the Moduli of Curves On the structure of certain valued fields II Random Cayley sum hypergraphs and $k$-fold sumsets