Root Numbers of Asai L-Functions

Abstract

Let E/F be a quadratic extension of p-adic fields. We compute the value of ∈(½, π, r, ψ) for a square integrable representation π of G L_n(E), which is (Galois) conjugate self-dual, where r denotes the Asai representation. This is the twisted version of a well-known result due to Bushnell and Henniart. The proof makes use of a result on the corresponding global root number, which is proved by a method conceived by Lapid and Rallis.