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arXiv · 2404.15716

Parity of the coefficients of certain eta-quotients, III: two special classes

William J. Keith·Fabrizio Zanello
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Abstract

We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related $q$-series. The present article focuses on two classes. One consists of eta-quotients of the form $f_t^3/f_1$, a distinguished case of Andrews' singular overpartitions that has recently attracted attention among researchers. In addition, we investigate the parity of certain pure eta-powers $f_1^t$, appending new results to known density theorems.

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William J. Keith, Fabrizio Zanello. 2024-04-24. Parity of the coefficients of certain eta-quotients, III: two special classes. https://arxiv.org/abs/2404.15716

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