Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows

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doi:10.3934/era.2019.26.002

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2019, Volume 26: 16-23. Doi: 10.3934/era.2019.26.002

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Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows

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1.
Département de Mathématiques, Université de Lille, Cité Scientifique, Villeneuve, D'Ascq, Cedex 9655, FR
2.
Department of Mathematics, University of Maryland, 4176 Campus Drive, College Park, MD 20742-4015, USA

Received: November 05, 2018

Revised: January 24, 2019

Published: March 2019

The first author is partially supported by the Labex CEMPI. The second author is supported by NSF grant DMS 1600687

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Abstract

We derive, from the work of M. Ratner on joinings of time-changes of horocycle flows and from the result of the authors on its cohomology, the property of orthogonality of powers for non-trivial smooth time-changes of horocycle flows on compact quotients. Such a property is known to imply P. Sarnak's Möbius orthogonality conjecture, already known for horocycle flows by the work of J. Bourgain, P. Sarnak and T. Ziegler.

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Mathematics Subject Classification: Primary: 11L20, 11N37; Secondary: 37D40.

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References

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