Par Kurlberg

KTH Stockholm KTH Stockholm

Distribution of lattice points on hyperbolic circles

Heilbronn Number Theory Seminar

3rd February 2021, 4:00 pm – 5:00 pm

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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