### Description

Abstract: With F. Andreatta we constructed p-adic L-functions attached to a triple (F, K, p) where F is a classical, elliptic modular eigenform, K a quadratic imaginary field and p a prime integer, all satisfying certain assumptions of which the most important is that p is not split in K. Such p adic L-functions have been constructed by N. Katz (during the 70') if F is an Eisenstein series and by Bertolini-Darmon-Prasana (2013) when F is a cuspform, when the prime p is split in K. I will also present some arithmetic applications of these constructions.