Sign-patterns of Certain Infinite Products

2025/07/22 by Timothy C. Huber, Huang, Zeyu, Huber, Timothy +8
Computer Science · #11F30 (Primary) 30C50 (Secondary) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.16644

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \frac(qⁱ;qⁱ)_∞(q^p;q^p)_∞ 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.

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