We consider three Coleman families of modular forms and we would like to construct a p-adic L-function interpolating the algebraic part of central values of the triple product L-function attached to these families and classical weights.

In this context there are more than one natural interpolation problems, and we can classify them in two types: balanced and unbalanced.

In this talk, we will explain the Greenberg-Seveso’s approach to solve the interpolation problems in the balanced case. This approach heavily relies on the nice overconvergent cohomology modules introduced by Ash and Stevens. Finally we would like to point out that one interesting fact that we find in this situation is that one single interpolation problem is solved by different p-adic L-functions at the same time.