TITLE: reference help needed on a fact about poles of L-functions
QUESTION [11 upvotes]: Suppose $\pi$ and $\rho$ are cuspidal automorphic representations on $GL(n)$ and $GL(m)$ respectively. Then the L-function $L(s,\pi \times \rho)$ has a pole iff and $m=n$ and $\pi$ is isomorphic to the contragradient of  $\rho$ by some twist. Does anyone know some reference containing the proof of this fact?
I checked Rankin-Selberg convolution paper by Jacquet-P.S-Shalika. It mentioned this result and said the proof would appear somewhere.
Many thanks.

REPLY [3 votes]: See also
C. Mœglin and J.-L. Waldspurger, Poles des fonctions L de paires pour GL(N), Appendice, Ann. Sci. École Norm. Sup. (4) 22 (1989), 667–674.