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Duke’s theorem for subcollections

Published online by Cambridge University Press:  02 October 2014

MENNY AKA
Affiliation:
Section de mathèmatiques, EPFL, Station 8 - Bât. MA, CH-1015 Lausanne, Switzerland email menashe-hai.akkaginosar@epfl.ch
MANFRED EINSIEDLER
Affiliation:
Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland email manfred.einsiedler@math.ethz.ch

Abstract

We combine effective mixing and Duke’s theorem on closed geodesics on the modular surface to show that certain subcollections of the collection of geodesics with a given discriminant still equidistribute. These subcollections are only assumed to have sufficiently large total length without any further restrictions.

Type
Research Article
Copyright
© Cambridge University Press, 2014 

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References

Bourgain, J. and Kontorovich, A.. Beyond expansion II: low-lying fundamental geodesics. Preprint, 2014, arXiv:1406.1366.Google Scholar
Duke, W.. Hyperbolic distribution problems and half-integral weight Maass forms. Invent. Math. 92(1) (1988), 7390.CrossRefGoogle Scholar
Einsiedler, M., Lindenstrauss, E., Michel, P. and Venkatesh, A.. Distribution of periodic torus orbits on homogeneous spaces. Duke Math. J. 148(1) (2009), 119174.CrossRefGoogle Scholar
Einsiedler, M., Lindenstrauss, E., Michel, P. and Venkatesh, A.. Distribution of periodic torus orbits and Duke’s Theorem for cubic fields. Ann. of Math. (2) 173(2) (2011), 815885.CrossRefGoogle Scholar
Einsiedler, M., Lindenstrauss, E., Michel, P. and Venkatesh, A.. The distribution of closed geodesics on the modular surface, and Duke’s Theorem. Enseign. Math. (2) 58(3–4) (2012), 249313.CrossRefGoogle Scholar
Einsiedler, M. and Ward, T.. Ergodic Theory—with a View Towards Number Theory (Graduate Texts in Mathematics, 259). Springer, Berlin, 2010.Google Scholar
Harcos, G.. Subconvex bounds for automorphic l-functions and applications. This is an unpublished dissertation. Available at http://www.renyi.hu/∼gharcos/ertekezes.pdf.Google Scholar
Harcos, G. and Michel, P.. The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points II. Invent. Math. 163(3) (2006), 581655.CrossRefGoogle Scholar
Howe, R. and Tan, E.-C.. Nonabelian harmonic analysis. Applications of SL(2,R). Springer, New York, 1992.Google Scholar
McMullen, C. T.. Uniformly Diophantine numbers in a fixed real quadratic field. Compos. Math. 145(4) (2009), 827844.CrossRefGoogle Scholar
Michel, P. and Venkatesh, A.. Equidistribution, L-functions and ergodic theory: on some problems of Yu Linnik. International Congress of Mathematicians, vol. II. European Mathematical Society, Zürich, 2006, pp. 421457.Google Scholar
Popa, A. A.. Central values of Rankin L-series over real quadratic fields. Compos. Math. 142(4) (2006), 811866.CrossRefGoogle Scholar
Venkatesh, A.. Sparse equidistribution problems, period bounds and subconvexity. Ann. of Math. (2) 172(2) (2010), 9891094.CrossRefGoogle Scholar
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