Subconvexity bounds for $\text{GL(3)}\times \text{GL(2)}$ $L$-functions in $\text{GL(2)}$ spectral aspect

Abstract

Let $\pi$ be a Hecke–Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ and $f$ be a holomorphic cusp form for $\mathrm{SL}(2,\mathbb{Z})$ of weight $k$ or a Hecke–Maass cusp form corresponding to the Laplacian eigenvalue $1/4+k^2$, $k\ge 1$, for $\mathrm{SL}(2,\mathbb{Z})$. In this paper, we prove the following subconvexity bound: