Congruences for Andrews-Beck partition statistics modulo powers of primes

被引：7
|
作者：
Mao, Renrong [1 ]
机构：
[1] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS | 2023年 / 146卷
基金：
中国国家自然科学基金;
关键词：
Rank; Congruences; Modular forms; Hecke operators; Andrews-Beck partition statistics;
D O I：
10.1016/j.aam.2023.102488
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let NT (m, k, n) denote the total number of parts in the partitions of n with rank congruent to m modulo k. Andrews recently provided a q-series proof of congruences for NT (m, k, n) modulo 5 and 7. In this paper, we establish congruences for NT (m, k, n) modulo powers of primes 8 >= 7. Our proof utilizes the Hecke operators. (c) 2023 Elsevier Inc. All rights reserved.
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页数：19
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