New arithmetic properties for overpartitions where nonoverlined parts are $\ell$-regular
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908398420754432 |
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| author | Nath, Hemjyoti Saikia, Manjil P. Sellers, James A. |
| author_facet | Nath, Hemjyoti Saikia, Manjil P. Sellers, James A. |
| contents | In this paper, we study the partition functions $\overline{R_\ell^\ast}(n)$, which count the number of overpartitions of $n$ where the non-overlined parts are $\ell$-regular for a given $\ell$. Using elementary techniques, as well as the theory of modular forms, we establish several new arithmetic properties, including infinite families of congruences for these functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New arithmetic properties for overpartitions where nonoverlined parts are $\ell$-regular Nath, Hemjyoti Saikia, Manjil P. Sellers, James A. Number Theory 11P81, 11P82, 11P83, 05A17, 11F11 In this paper, we study the partition functions $\overline{R_\ell^\ast}(n)$, which count the number of overpartitions of $n$ where the non-overlined parts are $\ell$-regular for a given $\ell$. Using elementary techniques, as well as the theory of modular forms, we establish several new arithmetic properties, including infinite families of congruences for these functions. |
| title | New arithmetic properties for overpartitions where nonoverlined parts are $\ell$-regular |
| topic | Number Theory 11P81, 11P82, 11P83, 05A17, 11F11 |
| url | https://arxiv.org/abs/2503.12145 |