Geodesic
Beyond expansion II: low-lying fundamental geodesics
Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1331-1359 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/694
Classification : 11-XX, 37-XX
Keywords: Affine sieve, closed geodesics, fundamental discriminants, equidistribution 
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     author = {Jean Bourgain and Alex Kontorovich},
     title = {Beyond expansion {II:} low-lying fundamental geodesics},
     journal = {Journal of the European Mathematical Society},
     pages = {1331--1359},
     year = {2017},
     volume = {19},
     number = {5},
     doi = {10.4171/jems/694},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/694/}
}
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Jean Bourgain; Alex Kontorovich. Beyond expansion II: low-lying fundamental geodesics. Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1331-1359. doi: 10.4171/jems/694

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