Vanishing coefficients in quotients of theta functions with odd moduli-Reference-Cited by-同舟云学术

Vanishing coefficients in quotients of theta functions with odd moduli

Published:2023-08-31 Issue:10 Volume:19 Page:2451-2481
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Du Julia Q. D.¹,Tang Dazhao²^ORCID

Affiliation:

1. School of Mathematical Sciences, Postdoctoral Research Station of Mathematics, Hebei Normal University, Shijiazhuang 050024, P. R. China

2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China

Abstract

Following recent studies of vanishing coefficients in arithmetic progressions in infinite [Formula: see text]-series products, we further prove that such phenomenon also exists in a family of quotients of theta functions with odd moduli. Moreover, we find that some arithmetic progressions with vanishing coefficients could be shared by an infinite family of quotients of theta functions. Finally, we present several related conjectures that merit further investigation.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Hebei Province

Chongqing Science and Technology Commission

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304212350121X

Reference21 articles.

1. Vanishing coefficients in infinite product expansions

2. Ramanujan’s Notebooks

3. The periodicity of the signs of the coefficients of certain infinite products

4. Finding Modular Functions for Ramanujan-Type Identities

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