ℓ-Divisibility of ℓ-regular partition functions

被引：0
|
作者：
Brian Dandurand
David Penniston
机构：
[1] Clemson University,Department of Mathematics
[2] Furman University,Department of Mathematics
来源：
The Ramanujan Journal | 2009年 / 19卷
关键词：
Partitions; Hecke eigenforms; 11P83;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give exact criteria for the ℓ-divisibility of the ℓ-regular partition function bℓ(n) for ℓ∈{5,7,11}. These criteria are found using the theory of complex multiplication. In each case the first criterion given corresponds to the Ramanujan congruence modulo ℓ for the unrestricted partition function, and the second is a condition given by J.-P. Serre for the vanishing of the coefficients of ∏m=1∞(1−qm)ℓ−1.
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页码：63 / 70
页数：7
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