Geodesic
Geometric invariants for real quadratic fields
W. Duke1 ; Ö. Imamoḡlu2 ; Á. Tóth3
1 University of California, Los Angeles, CA
2 Institute of Mathematics, ETH, Zürich, Switzerland
3 Eötvös Loránd University, Budapest, Hungary
Annals of mathematics, Tome 184 (2016) no. 3, pp. 949-990.

Voir la notice de l'article provenant de la source Annals of Mathematics website

To an ideal class of a real quadratic field we associate a certain surface. This surface, which is a new geometric invariant, has the usual modular closed geodesic as its boundary. Furthermore, its area is determined by the length of an associated backward continued fraction. We study the distribution properties of this surface on average over a genus. In the process we give an extension and refinement of the Katok-Sarnak formula.
DOI : 10.4007/annals.2016.184.3.8

W. Duke 1 ; Ö. Imamoḡlu 2 ; Á. Tóth 3

1 University of California, Los Angeles, CA
2 Institute of Mathematics, ETH, Zürich, Switzerland
3 Eötvös Loránd University, Budapest, Hungary 
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W. Duke; Ö. Imamoḡlu; Á. Tóth. Geometric invariants for real quadratic fields. Annals of mathematics, Tome 184 (2016) no. 3, pp. 949-990. doi : 10.4007/annals.2016.184.3.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.3.8/

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