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

Prahlad Sharma

Published 2020-10-20Version 1

Let $f$ be a $SL(2,\mathbb{Z})$ holomorhic Hecke form and $\pi$ be a $SL(3,\mathbb{Z})$ Maass cusp form with its Langlands parameter $\mu$ in generic position i.e. away from Weyl chamber walls and away from self dual forms. We study the second moment $\sum_{j} |L(1/2,\pi_j\times f)|^2$ and deduce the subconvexity bound \begin{equation*} L(1/2,\pi\times f)\ll_{f,\epsilon} \|\mu\|^{3/2-1/30+\epsilon} \end{equation*}