Hida families and p-adic triple product L-functions

摘要

We construct the three-variable p-adic triple product L-functions attached toHida families of ellptic newforms and prove the explicit interpolation formulaeat all critical specializations by establishing explicit Ichino's formulae forthe trilinear period integrals of automorphic forms. Our formulae perfectly fitthe conjectural shape of p-adic L-functions predicted by Coates andPerrin-Riou. As an application, we prove the factorization of certainunbalanced p-adic triple product L-functions into a product of anticyclotomicp-adic L-functions for modular forms. By this factorization, we give a newconstruction of the anticyclotomic p-adic L-functions for elliptic curves inthe definite case via the diagonal cycle Euler system 'a la Darmon and Rotgerand obtain a Greenberg-Stevens style proof of anticyclotomic exceptional zeroconjecture for elliptic curves due to Bertolini and Darmon.