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

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