Further results on arithmetic properties of biregular overpartitions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913813023948800 |
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| author | Ghoshal, Suparno Jana, Arijit |
| author_facet | Ghoshal, Suparno Jana, Arijit |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_21439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Further results on arithmetic properties of biregular overpartitions Ghoshal, Suparno Jana, Arijit Number Theory 11P83, 05A15, 05A17 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. |
| title | Further results on arithmetic properties of biregular overpartitions |
| topic | Number Theory 11P83, 05A15, 05A17 |
| url | https://arxiv.org/abs/2504.21439 |