Disjointness of moebius from horocycle flows

J. Bourgain, P. Sarnak, T. Ziegler

Research output: Chapter in Book/Report/Conference proceedingChapter

55 Scopus citations

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 Γ\SL2(ℝ), where Γ ⊂ SL2(ℝ) is a lattice.

Original languageEnglish (US)
Title of host publicationFrom Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publicationIn Memory of Leon Ehrenpreis
EditorsHershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Pages67-83
Number of pages17
DOIs
StatePublished - Sep 2 2013

Publication series

NameDevelopments in Mathematics
Volume28
ISSN (Print)1389-2177

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

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  • Cite this

    Bourgain, J., Sarnak, P., & Ziegler, T. (2013). Disjointness of moebius from horocycle flows. In H. Farkas, M. Knopp, R. Gunning, & B. A. Taylor (Eds.), From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis (pp. 67-83). (Developments in Mathematics; Vol. 28). https://doi.org/10.1007/978-1-4614-4075-8_5