TY - JOUR

T1 - Distribution of angles between geodesic rays associated with hyperbolic lattice points

AU - Boca, Florin P.

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2007/9

Y1 - 2007/9

N2 - 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].

AB - 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].

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U2 - 10.1093/qmath/ham014

DO - 10.1093/qmath/ham014

M3 - Article

AN - SCOPUS:34548410539

SN - 0033-5606

VL - 58

SP - 281

EP - 295

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 3

ER -