Arithmetic properties of $k$-tuple $\ell$-regular partitions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908358718521344 |
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| author | Nath, Hemjyoti Saikia, Manjil P. Sarma, Abhishek |
| author_facet | Nath, Hemjyoti Saikia, Manjil P. Sarma, Abhishek |
| contents | In this paper, we study arithmetic properties satisfied by the $k$-tuple $\ell$-regular partitions. A $k$-tuple of partitions $(ξ_1, ξ_2, \ldots, ξ_k)$ is said to be $\ell$-regular if all the $ξ_i$'s are $\ell$-regular. We study the cases $(\ell, k)=(2,3), (4,3), (\ell, p)$, where $p$ is a prime, and even the general case when both $\ell$ and $k$ are unrestricted. Using elementary means as well as the theory of modular forms we prove several infinite family of congruences and density results for these family of partitions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties of $k$-tuple $\ell$-regular partitions Nath, Hemjyoti Saikia, Manjil P. Sarma, Abhishek Number Theory 11P81, 11P82, 11P83, 05A17 In this paper, we study arithmetic properties satisfied by the $k$-tuple $\ell$-regular partitions. A $k$-tuple of partitions $(ξ_1, ξ_2, \ldots, ξ_k)$ is said to be $\ell$-regular if all the $ξ_i$'s are $\ell$-regular. We study the cases $(\ell, k)=(2,3), (4,3), (\ell, p)$, where $p$ is a prime, and even the general case when both $\ell$ and $k$ are unrestricted. Using elementary means as well as the theory of modular forms we prove several infinite family of congruences and density results for these family of partitions. |
| title | Arithmetic properties of $k$-tuple $\ell$-regular partitions |
| topic | Number Theory 11P81, 11P82, 11P83, 05A17 |
| url | https://arxiv.org/abs/2412.16193 |