Duke's Theorem for subcollections
Dynamical Systems
2019-02-20 v2 Number Theory
Abstract
We combine effective mixing and Duke's Theorem on closed geodesics on the modular surface to show that certain subcollections of the collection of geodesics with a given discriminant still equidistribute. These subcollections are only assumed to have sufficiently large total length without any further restrictions.
Cite
@article{arxiv.1403.2016,
title = {Duke's Theorem for subcollections},
author = {Menny Aka and Manfred Einsiedler},
journal= {arXiv preprint arXiv:1403.2016},
year = {2019}
}
Comments
Final version; to appear in Ergodic Theory and Dynamical Systems