Congruences modulo powers of 5 for Ramanujan's φ function

被引：0

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 50 条

[41] Congruences for cubic partition pairs modulo powers of 3
Lin, Bernard L. S.
Wang, Liuquan
Xia, Ernest X. W.
[J]. RAMANUJAN JOURNAL, 2018, 46 (02): : 563 - 578
[42] CONGRUENCES MODULO-5
KAPPUS, H
[J]. FIBONACCI QUARTERLY, 1986, 24 (02): : 181 - 182
[43] Congruences between modular forms modulo prime powers
Camporino, Maximilian
Pacetti, Ariel
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2018, 34 (04) : 1609 - 1643
[44] Some New Congruences Modulo 5 for the General Partition Function
B. R. Srivatsa Kumar
D. Shruthi
[J]. Russian Mathematics, 2020, 64 : 73 - 78
[45] CONGRUENCES MODULO POWERS OF 11 FOR SOME PARTITION FUNCTIONS
Wang, Liuquan
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (04) : 1515 - 1528
[46] Congruences for central factorial numbers modulo powers of prime
Wang, Haiqing
Liu, Guodong
[J]. SPRINGERPLUS, 2016, 5
[47] Some New Congruences Modulo 5 for the General Partition Function
Srivatsa Kumar, B. R.
Shruthi
Ranganatha, D.
[J]. RUSSIAN MATHEMATICS, 2020, 64 (07) : 73 - 78
[48] RAMANUJAN'S CUBIC CONTINUED FRACTION AND RAMANUJAN TYPE CONGRUENCES FOR A CERTAIN PARTITION FUNCTION
Chan, Hei-Chi
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (04) : 819 - 834
[49] Ramanujan-type congruences modulo 4 for partitions into distinct parts
Merca, Mircea
[J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2022, 30 (03): : 185 - 199
[50] ON THE RAMANUJAN-TYPE CONGRUENCES MODULO 8 FOR THE OVERPARTITIONS INTO ODD PARTS
Merca, Mircea
[J]. QUAESTIONES MATHEMATICAE, 2022, 45 (10) : 1567 - 1574

← 1 2 3 4 5 →