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 -