Beyond expansion, III: Reciprocal geodesics

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.

Locations

• Duke Mathematical Journal - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View