The distribution of closed geodesics on the modular surface, and Duke's theorem
Number Theory
2011-09-05 v1 Dynamical Systems
Abstract
We give an ergodic theoretic proof of a theorem of Duke about equidistribution of closed geodesics on the modular surface. The proof is closely related to the work of Yu. Linnik and B. Skubenko, who in particular proved this equidistribution under an additional congruence assumption on the discriminant. We give a more conceptual treatment using entropy theory, and show how to use positivity of the discriminant as a substitute for Linnik's congruence condition.
Keywords
Cite
@article{arxiv.1109.0413,
title = {The distribution of closed geodesics on the modular surface, and Duke's theorem},
author = {Manfred Einsiedler and Elon Lindenstrauss and Philippe Michel and Akshay Venkatesh},
journal= {arXiv preprint arXiv:1109.0413},
year = {2011}
}