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

2022/05/17 by Kim, Chan-Ho, Longo, Matteo
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.08080

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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• Two variable anticyclotomic p-adic L-functions for Hida families
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