On the Distribution of Angles between Geodesic Rays Associated with Hyperbolic Lattice Points
نویسنده
چکیده
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 [z1, 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 ˆ
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