New Ramanujan type congruences modulo 5 for overpartitions

被引：12

作者：

Dou, Donna Q. J. ^{[1
]}

Lin, Bernard L. S. ^{[2
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

[2] Jimei Univ, Sch Sci, Xiamen 361021, Peoples R China

来源：

RAMANUJAN JOURNAL | 2017年 / 44卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Partition; Overpartition; Congruence; Theta function; POWERS;

D O I：

10.1007/s11139-016-9782-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (p) over bar (n) denote the number of overpartitions of n. In this paper, we shall show that for n >= 0, (p) over bar (80n + r) equivalent to 0 (mod 5), where r = 8, 52, 68, and 72. In addition, we present a short alternative proof of the congruence (p) over bar (40n + 35) = 0 (mod 5), which is conjectured by Hirschhorn and Sellers.

引用

页码：401 / 410

页数：10

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