Pair correlation of angles between reciprocal geodesics on the modular surface
type: Item
instance of: scholarly article
title: Pair correlation of angles between reciprocal geodesics on the modular surface
zbMATH Open document ID: 1304.11073
author: Florin P. Boca
author: Alexandru A. Popa
author: Alexandru Zaharescu
author: Vicenţiu Paşol
published in: Algebra \& Number Theory
publication date: 2014-08-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1102.0328
review text: The authors prove a limit theorem for the pair correlation for angels between reciprocal geodesics on the modular surface. The main result gives a completely explicit formula for the pair correlation function containing natural geometric quantities. The method also gives further insight in the associated reciprocal classes of binary quadratic forms. The authors nicely explain the concept of reciprocal geodesics in the context of the underlying hyperbolic structure. The proof of the main result is rather elaborate, however the result itself is very interesting, since it is completely different from the Euclidean situation.
reviewed by: Robert F. Tichy
Mathematics Subject Classification ID: 11K36
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11M36
Mathematics Subject Classification ID: 11P21
zbMATH DE Number: 6331629
zbMATH Keywords: modular surface
zbMATH Keywords: reciprocal geodesics
zbMATH Keywords: pair correlation
zbMATH Keywords: hyperbolic lattice points
zbMATH Keywords: hyperbolic lattice angles
MaRDI profile type: Publication
OpenAlex ID: W3098902762
arXiv ID: 1102.0328
DOI: 10.2140/ANT.2014.8.999
description: scientific article; zbMATH DE number 6331629