@inbook{5e51207c4cbd49eabe48a7ba0b0844eb,

title = "Disjointness of moebius from horocycle flows",

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.",

keywords = "Disjointness of dynamical systems, Entropy, Moebius function, Randomness principle, Square-free flow, Vinogradov's bilinear sums",

author = "J. Bourgain and P. Sarnak and T. Ziegler",

year = "2013",

doi = "10.1007/978-1-4614-4075-8_5",

language = "English (US)",

isbn = "9781461440741",

series = "Developments in Mathematics",

pages = "67--83",

editor = "Hershel Farkas and Marvin Knopp and Robert Gunning and B.A Taylor",

booktitle = "From Fourier Analysis and Number Theory to Radon Transforms and Geometry",

}