Subconvexity for Rankin-Selberg L-Functions of Maass Forms

Abstract

In this paper we prove a subconvexity bound for Rankin–Selberg L-functions \(L(s,f \otimes g)\) associated with a Maass cusp form f and a fixed cusp form g in the aspect of the Laplace eigenvalue 1/4 + k2 of f, on the critical line Re s = 1/2. Using this subconvexity bound, we prove the equidistribution conjecture of Rudnick and Sarnak [RS] on quantum unique ergodicity for dihedral Maass forms, following the work of Sarnak [S2] and Watson [W]. Also proved here is that the generalized Lindelof hypothesis for the central value of our L-function is true on average.