Effective counting of simple closed geodesics on hyperbolic surfaces

Abstract

We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most L on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichmüller geodesic flow.

Locations

• arXiv (Cornell University) - View - PDF
• Journal of the European Mathematical Society - View - PDF