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arXiv · 2204.07364

Sum expressions for $p$-adic Hecke $L$-functions of totally real fields

Luochen Zhao
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Abstract

As a continuation of previous work, we establish sum expressions for $p$-adic Hecke $L$-functions of totally real fields in the sense of Delbourgo, assuming a totally real analog of Heegner hypothesis. This is done by finding explicit formulas of the periods of the corresponding $p$-adic measures. As an application, we extend the Ferrero-Greenberg formula of derivatives of $p$-adic $L$-functions to this setting.

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Luochen Zhao. 2022-04-15. Sum expressions for $p$-adic Hecke $L$-functions of totally real fields. https://arxiv.org/abs/2204.07364

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