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arXiv · 1406.1366

Beyond Expansion II: Low-Lying Fundamental Geodesics

Jean Bourgain·Alex Kontorovich
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Abstract

A closed geodesic on the modular surface is "low-lying" if it does not travel "high" into the cusp. It is "fundamental" 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.

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Jean Bourgain, Alex Kontorovich. 2014-06-05. Beyond Expansion II: Low-Lying Fundamental Geodesics. https://arxiv.org/abs/1406.1366

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