Distribution of a Certain Partition Function Modulo Powers of Primes

被引：29
|
作者：
Chan, Hei-Chi [1 ]
机构：
[1] Univ Illinois, Dept Math Sci, Springfield, IL 62703 USA
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 04期
关键词：
Distribution of partition function; Ono's theorem; Ramanujan's congruences; CONGRUENCES; CRANK; FORMS;
D O I：
10.1007/s10114-011-8620-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a certain partition function a(n) defined by Sigma(n >= 0) a(n) q(n) := Pi(n=1) (1 - q(n))(-1) (1 - q(2n))(-1). We prove that given a positive integer j >= 1 and a prime m >= 5, there are infinitely many congruences of the type a(An + B) 0 (mod m(j)). This work is inspired by Ono's ground breaking result in the study of the distribution of the partition function p(n).
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页码：625 / 634
页数：10
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