On the effective determination of Maass cusp forms by L-values

Abstract

Let f be a Hecke–Maass cusp form of Laplace eigenvalue 1/4+μ 2 with |μ|≤Λ for $\mathit{SL}_{2}(\mathbb{Z})$ . We show that f is uniquely determined by the central values of Rankin–Selberg L-functions L(s,f⊗g), where g runs over the set of holomorphic cusp forms of weight k≍ ϵ Λ 1+3θ+ϵ for any ϵ>0 for $\mathit{SL}_{2}(\mathbb{Z})$ .