New Ramanujan type congruences modulo 5 for overpartitions

被引：11
|
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
收藏
页码：401 / 410
页数：10
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