Beyond Expansion III: Reciprocal Geodesics
Number Theory
2019-12-19 v1
Abstract
We prove the existence of infinitely many low-lying and fundamental closed geodesics on the modular surface which are reciprocal, that is, invariant under time reversal. The method combines ideas from Parts I and II of this series, namely the dispersion method in bilinear forms, as applied to thin semigroups coming from restricted continued fractions.
Cite
@article{arxiv.1610.07260,
title = {Beyond Expansion III: Reciprocal Geodesics},
author = {Jean Bourgain and Alex Kontorovich},
journal= {arXiv preprint arXiv:1610.07260},
year = {2019}
}
Comments
21 pages, no figures