RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION

被引：47
|
作者：
Chan, Hei-Chi [1 ]
机构：
[1] Univ Illinois, Springfield, IL 62703 USA
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2010年 / 6卷 / 04期
关键词：
Ramanujan's cubic continued fraction; Ramanujan congruences; partition function; EXPLICIT EVALUATIONS; CONJECTURE; POWERS; PROOF;
D O I：
10.1142/S1793042110003241
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the divisibility of the function a(n) defined by Sigma(n >= 0) a(n)q(n) := (q;q)(infinity)(-1)(q(2); q(2))(infinity)(-1). In particular, we prove certain "Ramanujan type congruences" for a(n) modulo powers of 3.
引用
收藏
页码：819 / 834
页数：16
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