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On the Pair Correlation Density for Hyperbolic Angles

Authors
  • Kelmer, Dubi
  • Kontorovich, Alex
Type
Published Article
Publication Date
May 07, 2014
Submission Date
Aug 03, 2013
Identifiers
DOI: 10.1215/00127094-2861495
Source
arXiv
License
Yellow
External links

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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