Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields

Abstract

We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a 𝔭-adic distribution interpolating the special values of the twisted Rankin–Selberg L-function attached to cuspidal automorphic representations π and σ of GLn and GLn–1 over a number field k. If π and σ are ordinary at 𝔭, our distribution is bounded and yields analyticity of the associated 𝔭-adic L-function.