The local exterior square L-function: Holomorphy, non-vanishing and Shalika functionals

Let pi be a smooth, irreducible, square integrable representation of GL(m)(F), where F is a non-archimedean local field of characteristic zero. We prove that the exterior square L-function L-JS(s, pi, boolean AND(2)) defined via an integral representation due to Jacquet and Shalika is regular and non-vanishing in the region Re(s) > 0. We also investigate the behavior of the L-function L-JS(S, pi, boolean AND(2)) at s = 0, and show that if the function L-JS(s, pi, boolean AND(2)) has a pole at s = 0 then pi has a non-zero Shalika functional. (C) 2011 Elsevier Inc. All rights reserved.