Distribution of lattice points on hyperbolic circles

Abstract: 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 $\operatorname{PSL}(2,\mathbb Z)$, 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.

number theory

Audience: researchers in the topic

Heilbronn number theory seminar

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