Counting and equidistribution of reciprocal geodesics and dihedral groups

2022/04/21 by Viveka Erlandsson, Erlandsson, Viveka, Juan Souto +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2204.09956

openalex publication_date 2022/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the growth of the number of conjugacy classes of infinite dihedral subgroups of lattices in PSL(2,R), generalizing earlier work of Sarnak and Bourgain-Kontorovich on the growth of the number of reciprocal geodesics on the modular surface. We also prove that reciprocal geodesics are equidistributed in the unit tangent bundle.

Cited by

• Asymptotic growth of the number of Reciprocal Classes in the Hecke Groups
• Counting Reciprocal Hyperbolic Elements in Hecke Groups
• Counting and equidistribution of strongly reversible closed geodesics in negative curvature

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• Counting subgroups via Mirzakhani's curve counting
• Conjugacy geodesics and growth in dihedral Artin groups
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• Sums of Reciprocals of Fractional Parts II