Résume | In this talk, we will describe a method for assigning a $p$-adic $L$-function to a pair$(F,K)$, where $F$ is a Coleman family of modular forms and $K$ is a real quadratic field.This $p$-adic $L$-function interpolates central values of classical $L$-functions associatedto specializations of $F$ base changed to $K$. In certain situations, These $p$-adic$L$-functions display exceptional zero phenomena and encode information about algebraicpoints on modular abelian varieties. |