English

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 33 and powers of 22 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 88 which doesn't necessarily use any specific 22-dissection.

Keywords

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}
}