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arXiv · 2504.21439

Further results on arithmetic properties of biregular overpartitions

Suparno Ghoshal·Arijit Jana
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Abstract

Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for certain specific pairs of co-prime integers, while the paper [1] by Alanazi et al. investigated some congruences related to some similar and some different pairs of co-prime integers. In this paper we propose some elegant and elementary proofs of a subset of the congruences given in [1] by using only theta function and dissection identities. We also propose a generic method for proving congruences modulo $8$ which doesn't necessarily use any specific $2$-dissection.

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Suparno Ghoshal, Arijit Jana. 2025-04-30. Further results on arithmetic properties of biregular overpartitions. https://arxiv.org/abs/2504.21439

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