Simultaneous non-vanishing of GL(3)times GL(2) and GL(2) L-functions

Fix $g$ a Hecke-Maass form for $SL_3(\mathbb{Z})$. Let $q$ be any large prime number. In the family of holomorphic newforms $f$ of level $q$ and fixed weight, we find the average value of the product $L(\half,g\times f)L(\half,f)$. From this we derive a result on the simultaneous non-vanishing of these $L$-functions at the central point.