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arXiv · 1308.0754

On the Pair Correlation Density for Hyperbolic Angles

Dubi Kelmer·Alex Kontorovich
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Abstract

Let $\Gamma< \mathrm{PSL}_2(\mathbb{R})$ be a lattice and $\omega\in \mathbb{H}$ a point in the upper half plane. We prove the existence and give an explicit formula for the pair correlation density function for the set of angles between geodesic rays of the lattice $\Gamma \omega$ intersected with increasingly large balls centered at $\omega$, thus proving a conjecture of Boca-Popa-Zaharescu.

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Dubi Kelmer, Alex Kontorovich. 2013-08-03. On the Pair Correlation Density for Hyperbolic Angles. https://doi.org/10.1215/00127094-2861495

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