Sign Patterns of Certain Infinite Products

Authors

Zeyu Huang, Sun Yat-sen University
Timothy J. Huber, The University of Texas Rio Grande ValleyFollow
James McLaughlin, West Chester University of Pennsylvania
Pengjun Wang, Sun Yat-sen University
Yan Xu, Sun Yat-sen University
Dongxi Ye, Sun Yat-sen UniversityFollow

Document Type

Article

Publication Date

11-27-2025

Abstract

The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for

(qi;qi)∞(qp;qp)∞

for integers i>1 and primes p>3. The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of (q2;q2)∞(q5;q5)−1∞. The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al.

Comments

https://rdcu.be/eYnQ9

Recommended Citation

Huang, Zeyu, Timothy Huber, James McLaughlin, Pengjun Wang, Yan Xu, and Dongxi Ye. 2025. “Sign Patterns of Certain Infinite Products.” Annals of Combinatorics, ahead of print, November 27. https://doi.org/10.1007/s00026-025-00795-6

Publication Title

Annals of Combinatorics

DOI

10.1007/s00026-025-00795-6