Distribution of angles between geodesic rays associated with hyperbolic lattice points

Research output: Contribution to journalArticlepeer-review

Abstract

For every two points z0, Z1 in the upper-half plane ℍ, consider all elements γ in the principal congruence group Γ (N), acting on ℍ by fractional linear transformations, such that the hyperbolic distance between z1 and γz0 is at most R > 0. We study the distribution of angles between the geodesic rays [z 1, γz0] as R → ∞, proving that the limiting distribution exists independently of N and explicitly computing it. When z1 = z0, this is found to be the uniform distribution on the interval [-π/2, π/2].

Original languageEnglish (US)
Pages (from-to)281-295
Number of pages15
JournalQuarterly Journal of Mathematics
Volume58
Issue number3
DOIs
StatePublished - Sep 2007

ASJC Scopus subject areas

  • General Mathematics

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