l-adic properties of smallest parts functions

被引：27
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.
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页码：629 / 645
页数：17
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