The Second Moment of ${\mathrm{GL}}_3\times {\mathrm{GL}}_2$ $L$-functions at Special Points

Zhi Qi

Let $\ddot{I}•$ be a fixed Hecke--Maass form for ${\mathrm{SL}}_3(\mathbb{Z})$ and $u_j$ traverse an orthonormal basis of Hecke--Maass forms for ${\mathrm{SL}}_2(\mathbb{Z})$. Let $1/4+t_…