Equidistribution of $q$-orbits of closed geodesics
Abstract
Given an element of (\mathbb{Z}/q\mathbb{Z})^{\times} we associate a closed geodesic on the modular surface. We prove that the closed geodesics associated to cosets of sufficiently large subgroups equidistribute in the unit tangent bundle as q tends to infinity. This is a q -orbit analogue of Duke’s theorem for real quadratic fields as extended to subgroups by Popa. Finally, we show that the homology classes of the q -orbits of oriented closed geodesics concentrate around the Eisenstein line and present group theoretic applications.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Commentarii Mathematici Helvetici
- Volume
- 101
- Issue
- 4
- Pages
- 685–753
- Publication date
- 11 May 2026
- Language
- EN