The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points

Abstract

In this paper we solve the subconvexity problem for Rankin-Selberg $L$-functions $L(f\otimes g,s)$ where $f$ and $g$ are two cuspidal automorphic forms over $\mathbb{Q}$, $g$ being fixed and $f$ having large level and nontrivial nebentypus. We use this subconvexity bound to prove an equidistribution property for incomplete orbits of Heegner points over definite Shimura curves.