Proof of a conjecture on a congruence modulo 243 for overpartitions

被引：3

作者：

Huang, Xiaoqian ^{[1
]}

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

机构：

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

来源：

PERIODICA MATHEMATICA HUNGARICA | 2019年 / 79卷 / 02期

关键词：

Overpartitions; Congruences; Theta functions; THETA-FUNCTIONS; ANALOGS;

D O I：

10.1007/s10998-019-00283-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (p) over bar (n) denote the number of overpartitions of n. Recently, numerous congruences modulo powers of 2, 3 and 5 were established regarding (p) over bar (n). In particular, Xia discovered several infinite families of congruences modulo 9 and 27 for (p) over bar (n). Moreover, Xia conjectured that for n = 0, (p) over bar (96n + 76) = 0 (mod 243). In this paper, we confirm this conjecture by using theta function identities and the (p, k)-parametrization of theta functions.

引用

页码：227 / 235

页数：9

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