Pair correlation of angles between reciprocal geodesics on the modular surface

Details Pair correlation of angles between reciprocal geodesics on the modular surface Pair correlation of angles between reciprocal geodesics on the modular surface

2011-02-02

arxiv.org/abs/1102.0328v1

Mathematics

Number Theory

32 pages, 6 figures

Scientific paper

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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