Disjointness of moebius from horocycle flows

J. Bourgain, P. Sarnak*, T. Ziegler

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

91 Scopus citations


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 languageAmerican English
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
Number of pages17
StatePublished - 2013
Externally publishedYes

Publication series

NameDevelopments in Mathematics
ISSN (Print)1389-2177


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


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