New congruences modulo 5 for partition related to mock theta function ω(q)

被引：0

作者：

Lin, Bernard L. S. ^{[1
]}

Xiao, Jiejuan ^{[1
]}

机构：

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

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2021年 / 52卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Partition; Mock theta functions; congruence; Ramanujan's identity;

D O I：

10.1007/s13226-021-00078-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p(omega)(n) be the number of partitions of n in which each odd part is less than twice the smallest part, and assume that p(omega)(0) = 0. Andrews, Dixit, and Yee proved that the generating function of p(omega)(n) equals q(omega)(q), where omega(q) is one of the third order mock theta functions. Many scholars have studied the arithmetic properties of p(omega)(n). For example, Waldherr proved that p(omega)(40n + 28) p(omega)(40n + 36) 0(mod 5) by using the theory of Maass forms, which was later proved once again in an elementary method by Andrews, Passary, Sellers, and Yee. In this paper, we shall establish four new congruences modulo 5 for p(omega)(n).

引用

页码：141 / 148

页数：8

共 16 条

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