Windings of prime geodesics
Number Theory
2024-12-17 v3 Dynamical Systems
Geometric Topology
Abstract
The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. In this article, we introduce a new construction of winding numbers to record the winding of closed oriented geodesics about a prescribed cusp of a general cusped hyperbolic orbifold. For various arithmetic families of surfaces, this winding number can again be expressed by a Rademacher symbol, and access to the spectral theory of automorphic forms yields statistical results on the distribution of closed (primitive) oriented geodesics with respect to their winding.
Keywords
Cite
@article{arxiv.2209.06233,
title = {Windings of prime geodesics},
author = {Claire Burrin and Flemming von Essen},
journal= {arXiv preprint arXiv:2209.06233},
year = {2024}
}
Comments
Accepted version, 39p., to appear in IMRN