The first moment of GL(3)×GL(3) Rankin–Selberg <i>L</i> -functions

In this paper, we obtain an asymptotic formula for the average of Rankin–Selberg convolutions [Formula: see text] by using the [Formula: see text] Kuznetsov trace formula. Here G is a fixed Hecke–Maass cusp form for [Formula: see text] and F runs over an orthonormal basis of the space of Hecke–Maass cusp forms for [Formula: see text]. This implies the non-vanishing result of these L-functions at the central point.