Adic distributions attached to twisted tensor L-functions for GL2 over CM fields

Abstract

Let F be a totally real field. Let E be a quadratic extension that is totally imaginary over F. Let π be a cuspidal automorphic representation of cohomological type for over E. The properties of the twisted tensor L-function associated to π are studied in [6]. Special values of such functions are studied in [8] for and [9] for general F. Fix a prime in F. In this article we study special values of the twisted tensor L-function, , that is twisted by Hecke characters χ over F having -power conductor and . Specifically, we construct -adic distributions that interpolate these special values at certain critical points. This is proved under a certain non-vanishing hypothesis at infinity.