On the $p$-adic valuations of values of Legendre polynomials
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915286665396224 |
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| author | Alekseyev, Max A. Amdeberhan, Tewodros Shallit, Jeffrey Vukusic, Ingrid |
| author_facet | Alekseyev, Max A. Amdeberhan, Tewodros Shallit, Jeffrey Vukusic, Ingrid |
| contents | We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $p$-adic valuations of values of Legendre polynomials Alekseyev, Max A. Amdeberhan, Tewodros Shallit, Jeffrey Vukusic, Ingrid Number Theory We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017. |
| title | On the $p$-adic valuations of values of Legendre polynomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.08935 |