Arithmetic properties for (s, t) -regular bipartition functions

被引：7
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：
JOURNAL OF NUMBER THEORY | 2017年 / 171卷
基金：
美国国家科学基金会;
关键词：
Congruence; Regular partition; Bipartition; Ramanujan's theta function; CONGRUENCES; PARTITIONS;
D O I：
10.1016/j.jnt.2016.06.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let B-s,B-t(n) denote the number of (s, t)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for B-3,B-11(n). She also presented several conjectures on B-s,B-t(n). In this paper, utilizing an theta function identity appeared in Berndt's book, we confirm three conjectures on B-3,B-7(n) given by Dou. Moreover, we prove several infinite families of congruences modulo 3 and 5 for B-3,B-s(n) and B-5,B-s(n). In addition, we prove many infinite families of congruences modulo 7 for B-3,B-7(n) by employing an identity of Newman. (C) 2016 Elsevier Inc. All rights reserved.
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页码：1 / 17
页数：17
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