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

Chan-Ho Kim; Matteo Longo

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

Number Theory 2023-04-17 v3

Authors: Chan-Ho Kim , Matteo Longo

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.

Keywords

anticyclotomic p-adic L-functions Hida families modular forms Skinner-Urban L-function Gross points p-adic families central critical twist

Cite

@article{arxiv.2205.08080,
  title  = {An explicit comparison of anticyclotomic $p$-adic $L$-functions for Hida families},
  author = {Chan-Ho Kim and Matteo Longo},
  journal= {arXiv preprint arXiv:2205.08080},
  year   = {2023}
}

Comments

This version may be slightly different from the final version which will appear in IJNT

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

Abstract

Keywords

Cite

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