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arXiv · 1409.3764

Directions in hyperbolic lattices

Jens Marklof·Ilya Vinogradov
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Abstract

It is well known that the orbit of a lattice in hyperbolic $n$-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and express the limit distributions in terms of random hyperbolic lattices. This provides in particular a new perspective on recent results by Boca, Popa, and Zaharescu on 2-point correlations for the modular group, and by Kelmer and Kontorovich for general lattices in dimension $n=2$.

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Jens Marklof, Ilya Vinogradov. 2014-09-12. Directions in hyperbolic lattices. https://arxiv.org/abs/1409.3764

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