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

Let π be a smooth, irreducible, square integrable representation of GLm(F), where F is a non-archimedean local field of characteristic zero. We prove that the exterior square L-function LJS(s,π,∧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 LJS(s,π,∧2) at s=0, and show that if the function LJS(s,π,∧2) has a pole at s=0 then π has a non-zero Shalika functional.