On $7^k$-regular partitions modulo powers of $7$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909525265612800 |
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| author | Gireesh, D. S. B, HemanthKumar |
| author_facet | Gireesh, D. S. B, HemanthKumar |
| contents | In this study, we explore the arithmetic properties of $b_{7^k}(n)$ for any $k\geq1$, which enumerates the partitions of $n$ where no part is divisible by $7^k$. By constructing generating functions for $b_{7^k}(n)$ over specific arithmetic progressions, we establish a collection of Ramanujan-type congruences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $7^k$-regular partitions modulo powers of $7$ Gireesh, D. S. B, HemanthKumar Number Theory 11P83 (primary) 05A15, 05A17 (secondary) In this study, we explore the arithmetic properties of $b_{7^k}(n)$ for any $k\geq1$, which enumerates the partitions of $n$ where no part is divisible by $7^k$. By constructing generating functions for $b_{7^k}(n)$ over specific arithmetic progressions, we establish a collection of Ramanujan-type congruences. |
| title | On $7^k$-regular partitions modulo powers of $7$ |
| topic | Number Theory 11P83 (primary) 05A15, 05A17 (secondary) |
| url | https://arxiv.org/abs/2503.02366 |