CONGRUENCES FOR l-REGULAR PARTITIONS AND BIPARTITIONS

被引：1
|
作者：
Cui, Su-Ping [1 ,2 ]
Gu, Nancy S. S. [3 ]
机构：
[1] Qinghai Normal Univ, Sch Math & Stat, Xining, Qinghai, Peoples R China
[2] Acad Plateau Sci & Sustainabil, Xining, Qinghai, Peoples R China
[3] Nankai Univ, Ctr Combinator, LPMC, Tianjin, Peoples R China
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2020年 / 50卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Ramanujan's theta functions; partition congruences; l-regular partitions; l-regular bipartitions; ARITHMETIC PROPERTIES; MODULO POWERS; NUMBER;
D O I：
10.1216/rmj.2020.50.513
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Define F(q) := Sigma(infinity)(n=-infinity) (-1)(delta n) (an + b)q((cn2+dn)/2), which includes Ramanujan's theta function as a special case. We establish a dissection identity for this function, and use it to derive congruence properties for the coefficients of F (q). As an application we deduce several infinite families of congruences for l-regular partitions and l-regular bipartitions. In addition, we give a new proof of Ramanujan's congruence for the unrestricted partition function modulo 5.
引用
收藏
页码：513 / 526
页数：14
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