$p$-Adic hypergeometric functions and certain weight three newforms Article Swipe

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2403.16939

For an odd prime $p$ and a positive integer $n$, let ${_n}G_n[\cdots]_p$ denote McCarthy's $p$-adic hypergeometric function. In this article, we prove $p$-adic analogue of certain classical hypergeometric identities and using these identities we express the $p$-th Fourier coefficient of certain weight three newforms in terms of special values of ${_3}G_3[\cdots]_p$. Rodriguez-Villegas conjectured certain supercongruences between values of truncated hypergeometric series and the $p$-th Fourier coefficients of these newforms. As a consequence of our main results, we obtain another proof of these supercongruences which were earlier proved by Mortenson and Sun.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2403.16939
PDF: https://arxiv.org/pdf/2403.16939
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4393213757

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DOI: https://doi.org/10.48550/arxiv.2403.16939

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Title: $p$-Adic hypergeometric functions and certain weight three newforms

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-03-25

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Authors: Sulakashna, Rupam Barman

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Landing page: https://arxiv.org/abs/2403.16939

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PDF URL: https://arxiv.org/pdf/2403.16939

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Concepts: Conjecture, Mathematics, Combinatorics

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