Corpus ID: 221836650

# 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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