Determining cusp forms by central values of Rankin–Selberg L-functions

Let g be a fixed normalized Hecke–Maass cusp form for SL(2,Z) associated to the Laplace eigenvalue . We show that g is uniquely determined by the central values of the family for k sufficiently large, where Hk(1) denotes a Hecke basis of the space of holomorphic cusp forms for SL(2,Z).