Congruence Modulo 4 for Andrews' Even Parts Below Odd Parts Partition Function

被引：1

作者：

Chen, Dandan ^{[1
]}

Chen, Rong ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

来源：

ANNALS OF COMBINATORICS | 2023年 / 27卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Ternary quadratic form; Ramanujan-type congruences; Class number; TERNARY QUADRATIC-FORMS; INTEGER PARTITIONS; CLASS NUMBER; REPRESENTATIONS;

D O I：

10.1007/s00026-023-00645-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of (epsilon O) over bar (n) and further prove that (epsilon O) over bar (n) = 0 (mod 4) for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.

引用

页码：269 / 279

页数：11

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