Further results on vanishing coefficients in the series expansion of lacunary eta quotients

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
James McLaughlin
Dongxi Ye

Document Type

Article

Publication Date

10-5-2024

Abstract

In a previous paper the authors proved the existence of various pairs\break (A(q),B(q)) of lacunary eta quotients with identically vanishing coefficients. Further experiments indicated that the results in this previous paper were just the "tip of the iceberg". We provide a comprehensive description of what experiment suggests and employ a variety of methods to prove experimentally-derived results. The work is a template and atlas for the subsequent study of lacunary eta quotients. A broad range of proof strategies are applied to confirm the vanishing structure. These comprise a representative sample of techniques that may be used to study the remaining observations and conjectures resulting from the work.

Comments

Copyright the Authors.

Creative Commons Attribution 4.0 International License (CC BY 4.0)

Recommended Citation

Huber, Timothy, James McLaughlin, and Dongxi Ye. "Further results on vanishing coefficients in the series expansion of lacunary eta quotients." New York Journal of Mathematics 30 (2024): 1307-1436.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

New York Journal of Mathematics