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

共 50 条

[31] Products of special values of modular L-functions and their applications [J].

Chida, M .

ACTA ARITHMETICA, 2005, 116 (02) :99-114

[32] Families of Siegel modular forms, L-functions and modularity lifting conjectures [J].

Alexei Panchishkin .

Israel Journal of Mathematics, 2011, 185 :343-368

[33] p-adic Hodge theory and values of zeta functions of modular forms [J].

Kato, K .

ASTERISQUE, 2004, (295) :117-290

[34] TOPOLOGICAL MODULAR FORMS [J].

Goerss, Paul G. .

ASTERISQUE, 2010, (332) :221-255

[35] Generalized modular forms [J].

Knopp, M ;

Mason, G .

JOURNAL OF NUMBER THEORY, 2003, 99 (01) :1-28

[36] Weierstrass mock modular forms and elliptic curves [J].

Alfes C. ;

Griffin M. ;

Ono K. ;

Rolen L. .

Research in Number Theory, 1 (1)

[37] CONGRUENCES BETWEEN MODULAR FORMS AND RELATED MODULES [J].

Ciavarella, Miriam .

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2009, 41 (01) :55-70

[38] Algebraic modular forms [J].

Benedict H. Gross .

Israel Journal of Mathematics, 1999, 113 :61-93

[39] Congruences for Taylor expansions of quantum modular forms [J].

Pavel Guerzhoy ;

Zachary A Kent ;

Larry Rolen .

Research in the Mathematical Sciences, 1

[40] A modular invariant partition function for the fivebrane [J].

Dolan, L ;

Nappi, CR .

NUCLEAR PHYSICS B, 1998, 530 (03) :683-700

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