Pair correlation of hyperbolic lattice angles

Florin P. Boca; Alexandru A. Popa; Alexandru Zaharescu

doi:10.1142/S1793042114500651

Pair correlation of hyperbolic lattice angles

Florin P. Boca, Alexandru A. Popa, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let ω be a point in the upper half plane, and let be a discrete, finite covolume subgroup of PSLinf>2/inf> (R). We conjecture an explicit formula for the pair correlation of the angles between geodesic rays of the lattice ω, intersected with increasingly large balls centered at ω. We prove this conjecture for = PSL2(Z) and ω an elliptic point.

Original language	English (US)
Pages (from-to)	1955-1989
Number of pages	35
Journal	International Journal of Number Theory
Volume	10
Issue number	8
DOIs	https://doi.org/10.1142/S1793042114500651
State	Published - Dec 25 2014

Keywords

Hyperbolic lattice points
Pair correlation

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S1793042114500651

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title = "Pair correlation of hyperbolic lattice angles",

abstract = "Let ω be a point in the upper half plane, and let be a discrete, finite covolume subgroup of PSLinf>2/inf> (R). We conjecture an explicit formula for the pair correlation of the angles between geodesic rays of the lattice ω, intersected with increasingly large balls centered at ω. We prove this conjecture for = PSL2(Z) and ω an elliptic point.",

keywords = "Hyperbolic lattice points, Pair correlation",

author = "Boca, {Florin P.} and Popa, {Alexandru A.} and Alexandru Zaharescu",

note = "Funding Information: The first author was partly supported by CNCS-UEFISCDI grant PN-II-RU-TE-2011-3-0259. The second author was partly supported by European Community grant PIRG05-GA-2009-248569 and CNCS-UEFISCDI grant PN-II-RU-TE-2011-3-0259. Publisher Copyright: {\textcopyright} World Scientific Publishing Company.",

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language = "English (US)",

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AU - Boca, Florin P.

AU - Popa, Alexandru A.

AU - Zaharescu, Alexandru

N1 - Funding Information: The first author was partly supported by CNCS-UEFISCDI grant PN-II-RU-TE-2011-3-0259. The second author was partly supported by European Community grant PIRG05-GA-2009-248569 and CNCS-UEFISCDI grant PN-II-RU-TE-2011-3-0259. Publisher Copyright: © World Scientific Publishing Company.

PY - 2014/12/25

Y1 - 2014/12/25

N2 - Let ω be a point in the upper half plane, and let be a discrete, finite covolume subgroup of PSLinf>2/inf> (R). We conjecture an explicit formula for the pair correlation of the angles between geodesic rays of the lattice ω, intersected with increasingly large balls centered at ω. We prove this conjecture for = PSL2(Z) and ω an elliptic point.

AB - Let ω be a point in the upper half plane, and let be a discrete, finite covolume subgroup of PSLinf>2/inf> (R). We conjecture an explicit formula for the pair correlation of the angles between geodesic rays of the lattice ω, intersected with increasingly large balls centered at ω. We prove this conjecture for = PSL2(Z) and ω an elliptic point.

KW - Hyperbolic lattice points

KW - Pair correlation

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JF - International Journal of Number Theory

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Pair correlation of hyperbolic lattice angles

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