Proof of a conjectural congruence of Chan for Appell–Lerch sums-Reference-Cited by-同舟云学术

Proof of a conjectural congruence of Chan for Appell–Lerch sums

Published:2020-09-30 Issue:04 Volume:17 Page:1003-1011
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Fan Yan¹,Wang Liuquan²^ORCID,Xia Ernest X. W.¹

Affiliation:

1. Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China

2. School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P. R. China

Abstract

In 2012, Chan posed six conjectures on congruences for Appell–Lerch sums and five of them were proved by mathematicians. In this paper, we confirm the remaining conjectural congruence of Chan by utilizing an identity due to Hickerson and Mortenson and the theory of modular forms.

Funder

National Natural Science Foundation of China

Wuhan University

Nature Funds for Distinguished Young Scientists of Jiangsu Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042121500202

Reference13 articles.

1. Ramanujan's “lost” notebook VII: The sixth order mock theta functions

2. Sur les fonctions doublement périodiques de troisième espèce

3. Développements en série des fonctions doublement périodiques de troisième espèce

4. Sur les fonctions doublement périodiques de troisième espèce

5. Proofs of some conjectures of Chan on Appell–Lerch sums

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Proofs of conjectures of Chan for d(n);The Ramanujan Journal;2022-10-11