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arXiv · 2507.16644

Sign-patterns of Certain Infinite Products

Zeyu Huang·Timothy Huber·James McLaughlin·Pengjun Wang·Yan Xu·Dongxi Ye
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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 \[ \frac{(q^i;q^i)_{\infty}}{(q^p;q^p)_{\infty}} \] 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 \( (q^2;q^2)_{\infty}(q^5;q^5)_{\infty}^{-1} \). The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al.

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Zeyu Huang, Timothy Huber, James McLaughlin, Pengjun Wang, Yan Xu, Dongxi Ye. 2025-07-22. Sign-patterns of Certain Infinite Products. https://arxiv.org/abs/2507.16644

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