Further results on arithmetic properties of biregular overpartitions
Number Theory
2025-05-01 v1
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 and powers of 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 which doesn't necessarily use any specific -dissection.
Cite
@article{arxiv.2504.21439,
title = {Further results on arithmetic properties of biregular overpartitions},
author = {Suparno Ghoshal and Arijit Jana},
journal= {arXiv preprint arXiv:2504.21439},
year = {2025}
}