Equidistribution of partial coverings from closed geodesics

2025/02/12 by Asbjørn Christian Nordentoft, Nordentoft, Asbjørn Christian, Ser Peow Tan +1
Engineering · #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2502.08472

Abstract

Given a finite volume hyperbolic surface, a fundamental polygon and an oriented closed geodesic, we associate a partial covering of the surface. We prove that given a sequence of collections of oriented closed geodesics equidistributing in the unit tangent bundle then the associated partial coverings also equidistribute. In the case of the modular group, this yields an alternative proof of an equidistribution result due to Duke, Imamoglu, and Tóth.

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