Hello,


I began to read a few weeks ago an article about automorphic L-functions in which a formula like $L(s,\pi\times\pi')=L(s,\pi)L(s,\pi')$ appeared. Unfortunately, I can't find it back. Could someone give me some reference?
Thank you in advance.



Product of automorphic L-functions
As David Hansen says, Langlands proved that there is an automorphic representation (consisting of specific Eisenstein series) whose $L$-function is your right hand side. This representation is denoted by $\pi \boxplus \pi'$ and is called the isobaric sum of $\pi$ and $\pi'$, it mimics the direct sum of Galois representations. The notation $\pi\times\pi'$ or $\pi\otimes\pi'$ usually denotes the Rankin-Selberg convolution: it mimics the tensor product of Galois representations, and its $L$-function is not your right hand side.


