Extending Recent Congruence Results on $(\ell,μ)$-Regular Overpartitions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916763972665344 |
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| author | Paudel, Bishnu Sellers, James A. Wang, Haiyang |
| author_facet | Paudel, Bishnu Sellers, James A. Wang, Haiyang |
| contents | Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function $\overline{R_{\ell,μ}}(n)$, which enumerates the overpartitions of $n$ where no part is divisible by either $\ell$ or $μ$, for various integer pairs $(\ell, μ)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21989 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Recent Congruence Results on $(\ell,μ)$-Regular Overpartitions Paudel, Bishnu Sellers, James A. Wang, Haiyang Number Theory Combinatorics 11P83, 05A17 Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function $\overline{R_{\ell,μ}}(n)$, which enumerates the overpartitions of $n$ where no part is divisible by either $\ell$ or $μ$, for various integer pairs $(\ell, μ)$. 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. |
| title | Extending Recent Congruence Results on $(\ell,μ)$-Regular Overpartitions |
| topic | Number Theory Combinatorics 11P83, 05A17 |
| url | https://arxiv.org/abs/2505.21989 |