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arXiv · 2505.21989

Extending Recent Congruence Results on $(\ell,\mu)$-Regular Overpartitions

Bishnu Paudel·James A. Sellers·Haiyang Wang
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Abstract

Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function $\overline{R_{\ell,\mu}}(n)$, which enumerates the overpartitions of $n$ where no part is divisible by either $\ell$ or $\mu$, for various integer pairs $(\ell, \mu)$. In this paper, we substantially extend several of their results and establish infinitely many families of new congruences. Our proofs are entirely elementary, relying solely on classical $q$-series manipulations and dissection formulas.

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Bishnu Paudel, James A. Sellers, Haiyang Wang. 2025-05-28. Extending Recent Congruence Results on $(\ell,\mu)$-Regular Overpartitions. https://arxiv.org/abs/2505.21989

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