Subconvexity for Rankin-Selberg L-Functions of Maass Forms

In this paper we prove a subconvexity bound for Rankin–Selberg L-functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L(s,f \otimes g)$\end{document} 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 Lindelöf hypothesis for the central value of our L-function is true on average.