Explicit calculation of local integrals for twisted triple product L-functions

Abstract

Ichino proved a formula expressing global trilinear period integrals as products of central values of triple product $L$-functions and certain local trilinear integrals. In general, these local trilinear integrals are difficult to evaluate, and the main result in this article is to prove an identity relating local trilinear integrals and products of local Rankin–Selberg integrals in the twisted case. This result has applications to an explicit version of Ichino’s formula and the construction of $p$-adic $L$-functions for twisted triple products in our forthcoming works.