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arXiv · 2205.08080

An explicit comparison of anticyclotomic $p$-adic $L$-functions for Hida families

Chan-Ho Kim·Matteo Longo
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Abstract

The aim of this note is to compare several anticyclotomic $p$-adic $L$-functions for modular forms and $p$-adic families of ordinary modular forms, which have been defined and studied from different perspectives by Skinner-Urban, Hida, Perin-Riou, Bertolini-Darmon, Vatsal, Chida-Hsieh, Longo-Vigni, Castella-Longo and Castella-Kim-Longo. The main result of this paper is a comparison between the central critical twist of the two-variable anticyclotomic $p$-adic $L$-function obtained as specialisation of the three-variable $p$-adic $L$-function of Skinner-Urban and the two-variable $p$-adic $L$-function introduced by one of the authors on collaboration with Vigni by means of $p$-adic families of Gross points.

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Chan-Ho Kim, Matteo Longo. 2022-05-17. An explicit comparison of anticyclotomic $p$-adic $L$-functions for Hida families. https://arxiv.org/abs/2205.08080

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