乘子的Hecke关系和高阶最小部函数的同余

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-13 DOI:10.1016/j.jnt.2025.03.006

Clayton Williams

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引用次数: 0

摘要

我们从作用于爱森斯坦-埃塔商族的Hecke算子推导出恒等式，给出了这些商的系数的显式等式。从这些等式中我们推导出这些爱森斯坦商的系数的同余。作为应用，我们导出了几个高阶最小部函数模素幂的系统同余，解决了这些情况下的Garvan问题。我们还将曲柄矩和阶矩与配分函数模素幂联系起来。我们的一些结果加强和推广了Wang和Yang在2023年发表的论文。

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Hecke relations for eta multipliers and congruences for higher-order smallest parts functions

We derive identities from Hecke operators acting on a family of Eisenstein-eta quotients, giving explicit equalities relating the coefficients of these quotients. From these equalities we derive congruences for the coefficients of these Eisenstein-eta quotients modulo powers of primes. As an application we derive systematic congruences for several higher-order smallest parts functions modulo prime powers, resolving a question of Garvan for these cases. We also relate moments of cranks and ranks to the partition function modulo prime powers. Some of our results strengthen and generalize those of a 2023 paper by Wang and Yang.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.