Ramanujan-type congruences modulo 8 for 7-and 23-core partition functions

被引：0
|
作者：
Xia, Ernest X. W. [1 ]
Yao, Olivia X. M. [1 ]
机构：
[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China
来源：
RAMANUJAN JOURNAL | 2018年 / 47卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Congruences; t-Core partitions; Theta functions; CORE PARTITIONS; FACTS;
D O I：
10.1007/s11139-017-9898-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, Radu and Sellers proved numerous congruences modulo powers of 2 for -core partition functions by employing the theory of modular forms. In this paper, employing Ramanujan's theta function identities, we prove many infinite families of congruences modulo 8 for 7-core partition function. Our results generalize the congruences modulo 8 for 7-core partition function discovered by Radu and Sellers. Furthermore, we present new proofs of congruences modulo 8 for 23-core partition function. These congruences were first proved by Radu and Sellers.
引用
收藏
页码：221 / 235
页数：15
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