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

Abstract

We provide comparison results for anticyclotomic [Formula: see text]-adic [Formula: see text]-functions attached to Hida families of modular forms. The main result is a comparison between the anticyclotomic restriction of the three variable [Formula: see text]-adic [Formula: see text]-function introduced by Skinner and Urban, and the anticyclotomic [Formula: see text]-function constructed by means of [Formula: see text]-adic families of Gross points in the setting of definite quaternion algebras. Several auxiliary results involving anticyclotomic [Formula: see text]-adic [Formula: see text]-functions introduced by Chida-Hsieh and Büyükboduk–Lei are also proved.