Let $\pi=\pi_1 \otimes \pi_2 \otimes \pi_3$ be a unitary cuspidal automorphic representation of $\mathrm{ GL}_3^3(\mathbb{ A}_F)$ where $F$ is a number field. Assume that $\pi$ is everywhere tempered. Under suitable local hypotheses, for a sufficiently large finite set of places $S$ of $F$ we prove that the triple product $L$-function $L^S(s,\pi,\otimes^3)$ admits a meromorphic continuation to $\mathrm{ Re}(s) >\tfrac{ 1}{ 2}$. We also give some information about the possible poles.
Categories: math.NT