Incongruences for modular forms and applications to partition functions

被引：4

作者：

Garthwaite, Sharon Anne ^{[1
]}

Jameson, Marie ^{[2
]}

机构：

[1] Bucknell Univ, Dept Math, Lewisburg, PA 17837 USA

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

ADVANCES IN MATHEMATICS | 2021年 / 376卷

关键词：

Modular form; Incongruence; Partition function; Generalized Frobenius partition; Mock theta function; MOCK THETA-FUNCTIONS; CONGRUENCES; RAMANUJAN;

D O I：

10.1016/j.aim.2020.107448

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The study of arithmetic properties of coefficients of modular forms f(tau) = Sigma a(n)q(n) has a rich history, including deep results regarding congruences in arithmetic progressions. Recently, work of C.-S. Radu, S. Ahlgren, B. Kim, N. Andersen, and S. Lobrich have employed the q-expansion theory of P. Deligne and M. Rapoport in order to determine more about where these congruences can occur. Here, we apply the method to a large class of modular forms, and in particular to several noteworthy examples, including generalized Frobenius partitions and the two mock theta functions f (q) and omega (q). (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：17

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