[Abstract] Zhumagali Shomanov and Frank Garvan, An infinite family of overpartition congruences mod powers of $2$ , The Ramanujan Journal, 68 (2025), 115 (17 pages).
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 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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Created by F.G. Garvan (fgarvan@ufl.edu) on Saturday, December 6, 2025.
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