Let $G$ be a reductive group over the adele ring $\mathbb A_F$ of a number field $F$. Let also $r$ be a complex finite dimensional representation of the $L$-group $r:{^LG}\to GL(V)$.
It is generally known that for a tempered automorphic representation $\pi = \otimes ' \pi_v$ (meaning that the local constituents $\pi_v$ are tempered for all $v$), then the automorphic $L$-function $L(s,\pi,r)$ is holomorphic for Re$(s)>1$. But is there a good, concrete reference for this that I may cite for this? Or perhaps the proof of this is much easier than I am expecting?
