We use the doubling method to construct p-adic L-functions for finite-slope families of automorphic forms on symplectic and unitary groups. A key construction is the p-adic deformation of iterations of Maass-Shimura differential operators on nearly overconvergent families. We will explain how to generalize the construction for GL(2) by Andreatta and Iovita, and how to bypass explicit computations of formulas of iterations of differential operators on q-expansions by using dynamics of U_p operators.

I will give an introduction to p-adic L-functions. I will explain the conjecture by Coates and Perrin-Riou on the existence of p-adic L-functions and their definition of the modified Euler factors at p for p-adic interpolations. I will also talk about some approaches for constructing p-adic L-functions with some examples.