Simultaneous non-vanishing of central values of $\mathrm{GL}(2)\times \mathrm{GL}(3)$ and $\mathrm{GL}(3)\times \mathrm{GL}(3)$ $L$-functions

Junjie Pan

Let $g$ denote a fixed holomorphic Hecke cusp form of weight $k\equiv 0(\mathrm{mod}4)$ on ${\mathrm{SL}}_2(\mathbb{Z})$, and let $\pi$ be a fixed cuspidal automorphic representation of $\m…