# On the distribution of lattice points on hyperbolic circles

@article{Chatzakos2020OnTD, title={On the distribution of lattice points on hyperbolic circles}, author={Dimitrios Chatzakos and Par Kurlberg and Stephen Lester and Igor Wigman}, journal={arXiv: Number Theory}, year={2020} }

We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane $\mathbb{H}$. The angles of lattice points arising from the orbit of the modular group $PSL_{2}(\mathbb{Z})$, and lying on hyperbolic circles, are shown to be equidistributed for generic radii. However, the 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…

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