Equidistribution of geodesics on homology classes and analogues for free groups
Number Theory
2007-05-23 v3
Abstract
We investigate how often geodesics have homology in a fixed set of the homology lattice of a compact Riemann surface. We prove that closed geodesics are equidistributed on any sets with asymptotic density with respect to a specific norm. We explain the analogues for free groups, conjugacy classes and discrete logarithms, in particular, we investigate the density of conjugacy classes with relatively prime discrete logarithms.
Keywords
Cite
@article{arxiv.math/0509513,
title = {Equidistribution of geodesics on homology classes and analogues for free groups},
author = {Yiannis Petridis and Morten S. Risager},
journal= {arXiv preprint arXiv:math/0509513},
year = {2007}
}
Comments
24 pages, 2 figures. Changes: Include a reference to a preprint of Collier and Sharp where they apply our techniques to variable curvature. Corrected a lemma which Collier and Sharp pointed out was wrong. Our main theorem changed accordingly