### Distribution of lattice points on hyperbolic circles

Heilbronn Number Theory Seminar

3rd February 2021, 4:00 pm – 5:00 pm

Zoom,

We study the distribution of lattice points lying on expanding circles

in the hyperbolic plane. The angles of lattice points arising from the

orbit of the modular group PSL(2,Z), and lying on hyperbolic circles

centered at i, are shown to be equidistributed for generic radii

(among the ones that contain points). We also show that angles fail to

equidistribute on a thin set of exceptional radii, even in the

presence of growing multiplicity. Surprisingly, the distribution of

angles on hyperbolic circles turns out to be related to the angular

distribution of euclidean lattice points lying on circles in the

plane, along a thin subsequence of radii. This is joint work with

D. Chatzakos, S. Lester and I. Wigman.

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