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arXiv · 2510.20175

An infinite family of overpartition congruences mod powers of 2

Zhumagali Shomanov·Frank Garvan
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Abstract

We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's $U_2$ operator, we determine lower bounds on the 2-adic valuations of the coefficients that arise at each step. Our approach yields new modular equations relating the Hauptmoduln $G_2$ on $\Gamma_0(2)$ and $G_8$ on $\Gamma_0(8)$, together with explicit $U_2$-action formulas.

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Zhumagali Shomanov, Frank Garvan. 2025-10-23. An infinite family of overpartition congruences mod powers of 2. https://arxiv.org/abs/2510.20175

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