Dissections of lacunary eta quotients and identically vanishing coefficients

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
James McLaughlin, West Chester University of Pennsylvania
Dongxi Ye, Sun Yat-sen UniversityFollow

Document Type

Article

Publication Date

7-2025

Abstract

For any function A(q)=∑∞n=0anqn defineA(0):={n∈N:an=0}.Now suppose C(q) and D(q) are two functions whose m-dissections are given byC(q)=c0G0(qm)+c1qG1(qm)+…+cm−1qm−1Gm−1(qm),D(q)=d0G0(qm)+d1qG1(qm)+…+dm−1qm−1Gm−1(qm).If it is the case that ci=0⟺di=0, i=0,1,…,m−1, then we say that C(q) and D(q) have similar m-dissections, and then it is also clear that C(0)=D(0), in which case we say that C(q) and D(q) have identically vanishing coefficients. In the present paper some new 4-dissections of particular eta quotients are developed. These are used in conjunction with known 2- and 3-dissections to prove many results on the identical vanishing of coefficients of various eta quotients, results which were found experimentally and partially proved in another paper by the present authors. Similar arguments allow many results of the form C(0)⫋D(0) to be proved for many pairs of lacunary eta quotients C(q) and D(q).

Comments

Original published version available at https://doi.org/10.1016/j.aam.2025.102902

Recommended Citation

Huber, Tim, James McLaughlin, and Dongxi Ye. "Dissections of lacunary eta quotients and identically vanishing coefficients." Advances in Applied Mathematics 168 (2025): 102902. https://doi.org/10.1016/j.aam.2025.102902

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Advances in Applied Mathematics

DOI

10.1016/j.aam.2025.102902