Congruences modulo 16, 32, and 64 for Andrews's singular overpartitions

被引：21

作者：

Yao, Olivia X. M. ^{[1
]}

机构：

[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China

来源：

RAMANUJAN JOURNAL | 2017年 / 43卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Singular overpartitions; Arithmetic properties; Theta functions; ANALOGS;

D O I：

10.1007/s11139-015-9760-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a recent work, Andrews gave a definition of combinatorial objects which he called singular overpartitions and proved that these singular overpartitions, which depend on two parameters k and i, can be enumerated by the function which denotes the number of overpartitions of n in which no part is divisible by k and only parts may be overlined. Andrews, Chen, Hirschhorn and Sellers, and Ahmed and Baruah discovered numerous congruences modulo 2, 3, 4, 8, and 9 for . In this paper, we prove a number of congruences modulo 16, 32, and 64 for (C) over bar3,1 (n).

引用

页码：215 / 228

页数：14