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arXiv · 2507.01836

$p$-adic moments of $L$-functions

Daniel Kriz·Asbjørn Christian Nordentoft
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Abstract

We obtain a formula for the $p$-adic valuation of weighted moments of central $L$-values of holomorphic cusp forms twisted by Dirichlet characters of order $p$. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal $p$-adic measure into a vertical one, applied to the horizontal $p$-adic $L$-functions as defined by the authors in previous work.

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Daniel Kriz, Asbjørn Christian Nordentoft. 2025-07-02. $p$-adic moments of $L$-functions. https://arxiv.org/abs/2507.01836

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