Beyond expansion II: low-lying fundamental geodesics
Jean BourgainInstitute for Advanced Study, Princeton, USA
Alex KontorovichYale University, New Haven, USA
A closed geodesic on the modular surface is "low-lying" if it does not travel"high" into the cusp. It is "undamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many low-lying fundamental geodesics, answering a question of Einsiedler–Lindenstrauss–Michel–Venkatesh.
Cite this article
Jean Bourgain, Alex Kontorovich, Beyond expansion II: low-lying fundamental geodesics. J. Eur. Math. Soc. 19 (2017), no. 5, pp. 1331–1359DOI 10.4171/JEMS/694