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This is a Quantitative Study study.

September 23, 2025Open Access

Sign-patterns of Certain Infinite Products

Key Points

The analysis reveals sign patterns of Fourier coefficients, extending known conjectures in the field.
Characterization focuses on the sign distribution of coefficients for specific eta quotients, particularly involving prime integers.
Methodological approaches utilize expansions for theta functions alongside dissection formulas of quintuple products.
Findings support and expand on multiple conjectures proposed by Bringmann et al. regarding eta quotients.

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.

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Cite This Study

Huang et al. (Tue,) studied this question.

synapsesocial.com/papers/68d4759031b076d99fa6d658 https://doi.org/https://doi.org/10.48550/arxiv.2507.16644

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