On the tempered spectrum of quasi-split classical groups

Abstract. We determine the poles of the standard intertwining operators for a maximal parabolic sub-group of the quasi-split unitary group defined by a quadratic extension E/F of p-adic fields of char-acteristic zero. We study the case where the Levi component M GLn(E) × Um(F), with n ≡ m (mod 2). This, along with earlier work, determines the poles of the local Rankin-Selberg product L-function L(s, τ ′ × τ), with τ ′ an irreducible unitary supercuspidal representation of GLn(E) and τ a generic irreducible unitary supercuspidal representation of Um(F). The results are interpreted using the theory of twisted endoscopy