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15 June 2004 On the uniform equidistribution of long closed horocycles
Andreas Strömbergsson
Duke Math. J. 123(3): 507-547 (15 June 2004). DOI: 10.1215/S0012-7094-04-12334-6

Abstract

It is well known that on any given hyperbolic surface of finite area, a closed horocycle of length becomes asymptotically equidistributed as →∞. In this paper we prove that any subsegment of length greater than 1/2 + ε of such a closed horocycle also becomes equidistributed as →∞. The exponent 1/2 + ε is the best possible and improves upon a recent result by Hejhal [He3]. We give two proofs of the above result; our second proof leads to explicit information on the rate of convergence. We also prove a result on the asymptotic joint equidistribution of a finite number of distinct subsegments having equal length proportional to .

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Andreas Strömbergsson. "On the uniform equidistribution of long closed horocycles." Duke Math. J. 123 (3) 507 - 547, 15 June 2004. https://doi.org/10.1215/S0012-7094-04-12334-6

Information

Published: 15 June 2004
First available in Project Euclid: 11 June 2004

zbMATH: 1060.37023
MathSciNet: MR2068968
Digital Object Identifier: 10.1215/S0012-7094-04-12334-6

Subjects:
Primary: 37D40
Secondary: 11F , 30F35

Rights: Copyright © 2004 Duke University Press

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Vol.123 • No. 3 • 15 June 2004
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