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Duke’s theorem for subcollections

Published online by Cambridge University Press:  02 October 2014

MENNY AKA  and
MANFRED EINSIEDLER
MENNY AKA
Affiliation:
Section de mathèmatiques, EPFL, Station 8 - Bât. MA, CH-1015 Lausanne, Switzerland email [email protected]
MANFRED EINSIEDLER
Affiliation:
Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland email [email protected]
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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
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 2 , April 2016 , pp. 335 - 342
Copyright
© Cambridge University Press, 2014 

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