Bounds for the spectral mean value of central values of L-functions

We give a new proof of the known subconvexity bound of spectral mean values of some GL(2) L-functions at coming from the Rankin–Selberg L-functions of a GL(3) Eisenstein series and a GL(2) or Γ0(q) Maass form, as well as a new result in the twisted case. This is inspired by X. Liʼs result on the bounds for GL(3)×GL(2) L-functions of Hecke–Maass forms.