Beyond expansion II: low-lying fundamental geodesics

Abstract

A closed geodesic on the modular surface is "low-lying" if it does not travel"high" into the cusp. It is "undamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many low-lying fundamental geodesics, answering a question of Einsiedler–Lindenstrauss–Michel–Venkatesh.