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

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2018-11-12 DOI:10.3934/ERA.2019.26.002

L. Flaminio, G. Forni

引用次数: 11

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 Mobius orthogonality conjecture, already known for horocycle flows by the work of J. Bourgain, P. Sarnak and T. Ziegler.

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环流平滑时间变化的正交幂和Möbius猜想

从M. Ratner关于环流时变的联结的工作和作者关于环流上同调的结果，导出了紧商上环流非平凡光滑时变幂的正交性。这种性质被认为暗示了P. Sarnak的莫比乌斯正交猜想，该猜想已经被J. Bourgain、P. Sarnak和T. Ziegler的工作所知。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007