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

Abstract

We study simultaneous non-vanishing of $L(\tfrac{1}{2},\di)$ and $L(\tfrac{1}{2},g\otimes \di)$, when $\di$ runs over an orthogonal basis of the space of Hecke-Maass cusp forms for $SL(3,\mathbb{Z})$ and $g$ is a fixed $SL(2,\mathbb{Z})$ Hecke cusp form of weight $k\equiv 0(\mathrm{mod}4)$.

Comments are welcome!

References in corpus (1)

• Simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass L-functions