Formula omitted]-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 GL2 over E. The properties of the twisted tensor L-function L(s,π,As) associated to π are studied in [6]. Special values of such functions are studied in [8] for F=Q and [9] for general F. Fix a prime p in F. In this article we study special values of the twisted tensor L-function, L(s,π,χ,As), that is twisted by Hecke characters χ over F having p-power conductor and χ∞=1. Specifically, we construct p-adic distributions that interpolate these special values at certain critical points. This is proved under a certain non-vanishing hypothesis at infinity.Our results here generalize earlier work by the author and Eknath Ghate for E an imaginary quadratic extension (see [2]).