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.

Authors

Philippe Michel

Department of Mathematics
Université Montpellier II
34095 Montpellier
France