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.