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arXiv · 1102.0328

Pair correlation of angles between reciprocal geodesics on the modular surface

Florin P. Boca·Vicentiu Pasol·Alexandru A. Popa·Alexandru Zaharescu
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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 P. Boca, Vicentiu Pasol, Alexandru A. Popa, Alexandru Zaharescu. 2013-11-24. Pair correlation of angles between reciprocal geodesics on the modular surface. https://doi.org/10.2140/ant.2014.8.999

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