  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 $k\equiv 0 \pmod 4$.
