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2014 Pair correlation of angles between reciprocal geodesics on the modular surface
Florin Boca, Vicenţiu Paşol, Alexandru Popa, Alexandru Zaharescu
Algebra Number Theory 8(4): 999-1035 (2014). DOI: 10.2140/ant.2014.8.999

Abstract

The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as well as arithmetic information about the associated reciprocal classes of binary quadratic forms. One striking feature is the absence of a gap beyond zero in the limiting distribution, contrasting with the analog Euclidean situation.

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Florin Boca. Vicenţiu Paşol. Alexandru Popa. Alexandru Zaharescu. "Pair correlation of angles between reciprocal geodesics on the modular surface." Algebra Number Theory 8 (4) 999 - 1035, 2014. https://doi.org/10.2140/ant.2014.8.999

Information

Received: 3 September 2013; Revised: 21 October 2013; Accepted: 22 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1304.11073
MathSciNet: MR3248992
Digital Object Identifier: 10.2140/ant.2014.8.999

Subjects:
Primary: 11K36
Secondary: 11J71, 11M36, 11P21, 37D40

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.8 • No. 4 • 2014
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