a""-Divisibility of a""-regular partition functions

被引：39
|
作者：
Dandurand, Brian [2 ]
Penniston, David [1 ]
机构：
[1] Furman Univ, Dept Math, Greenville, SC 29613 USA
[2] Clemson Univ, Dept Math, Clemson, SC 29634 USA
来源：
RAMANUJAN JOURNAL | 2009年 / 19卷 / 01期
关键词：
Partitions; Hecke eigenforms;
D O I：
10.1007/s11139-007-9042-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give exact criteria for the a""-divisibility of the a""-regular partition function b (a"") (n) for a""a{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 a"" for the unrestricted partition function, and the second is a condition given by J.-P. Serre for the vanishing of the coefficients of R (m=1) (az) (1-q (m) ) (a""-1).
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页码：63 / 70
页数：8
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