English

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.

Keywords

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

R2 v1 2026-06-22T16:29:04.376Z