English

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.

Keywords

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

R2 v1 2026-06-21T17:20:19.328Z