The second moment of GL(3)×GL(2) L-functions, integrated

We consider the family of Rankin–Selberg convolution L-functions of a fixed SL(3,Z) Maass form with the family of Hecke–Maass cusp forms on SL(2,Z). We estimate the second moment of this family of L-functions with a “long” integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T12).