l-adic properties of smallest parts functions

被引：28

作者：

Ahlgren, Scott ^{[1
]}

Bringmann, Kathrin ^{[2
]}

Lovejoy, Jeremy ^{[3
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Cologne, Math Inst, D-50931 Cologne, Germany

[3] Univ Paris 07, LIAFA, CNRS, F-75205 Paris 13, France

来源：

ADVANCES IN MATHEMATICS | 2011年 / 228卷 / 01期

关键词：

Congruences; Partitions; Overpartitions; Smallest parts functions; Mock modular forms; Harmonic weak Maass forms; Hecke operators;

D O I：

10.1016/j.aim.2011.05.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove explicit congruences modulo powers of arbitrary primes for three smallest parts functions: one for partitions, one for overpartitions, and one for partitions without repeated odd parts. The proofs depend on l-adic properties of certain modular forms and mock modular forms of weight 3/2 with respect to the Hecke operators T (l(2m)). (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：629 / 645

页数：17

共 18 条

[1] Distribution of the partition function module composite integers M [J].