Congruences modulo powers of 5 for Ramanujan's φ function

被引：1

作者：

Du, Julia Q. D. ^{[1
]}

Tang, Dazhao ^{[2
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Hebei Key Lab Computat Math & Applicat, Shijiazhuang 050024, Peoples R China

[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 537卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Congruences; Ramanujan phi function; Modular forms; PARTITIONS; IDENTITIES;

D O I：

10.1016/j.jmaa.2024.128260

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 2012, Chan proved a number of congruences with different moduli for the coefficients of Ramanujan's phi function. In particular, he obtained a congruence modulo 5. Chan further conjectured three congruences modulo 25 for the coefficients of Ramanujan's phi function. In 2019, Baruah and Begum not only confirmed three conjectural congruences due to Chan, but also established three congruences modulo 125 for this function. In this paper, utilizing the Atkin U-operator and the theory of modular forms, we establish several infinite families of congruences modulo any powers of 5 for the coefficients of Ramanujan's phi function. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：18

共 30 条

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