Pair correlation of angles between reciprocal geodesics on the modular surface
Number Theory
2016-01-20 v4 Dynamical Systems
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.
Cite
@article{arxiv.1102.0328,
title = {Pair correlation of angles between reciprocal geodesics on the modular surface},
author = {Florin P. Boca and Vicentiu Pasol and Alexandru A. Popa and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:1102.0328},
year = {2016}
}
Comments
27 pages, 6 figures. Version accepted for publication