Disjointness of Moebius from Horocycle Flows

Chapter
Part of the Developments in Mathematics book series (DEVM, volume 28)

Abstract

We formulate and prove a finite version of Vinogradov’s bilinear sum inequality. We use it together with Ratner’s joinings theorems to prove that the Moebius function is disjoint from discrete horocycle flows on \(\Gamma \setminus S{L}_{2}(\mathbb{R})\), where \(\Gamma \subset S{L}_{2}(\mathbb{R})\) is a lattice.

Key words

Moebius function Randomness principle Vinogradov’s bilinear sums Entropy Square-free flow Disjointness of dynamical systems 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsTechnion - Israel Institute of TechnologyHaifaIsrael

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