Disjointness of moebius from horocycle flows

J. Bourgain; P. Sarnak; T. Ziegler

doi:10.1007/978-1-4614-4075-8_5

Disjointness of moebius from horocycle flows

J. Bourgain, P. Sarnak, T. Ziegler

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

94 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 language	English (US)
Title of host publication	From Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publication	In Memory of Leon Ehrenpreis
Editors	Hershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Pages	67-83
Number of pages	17
DOIs	https://doi.org/10.1007/978-1-4614-4075-8_5
State	Published - 2013

Publication series

Name	Developments in Mathematics
Volume	28
ISSN (Print)	1389-2177

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

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

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10.1007/978-1-4614-4075-8_5

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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.",

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Disjointness of moebius from horocycle flows. / Bourgain, J.; Sarnak, P.; Ziegler, T.
From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis. ed. / Hershel Farkas; Marvin Knopp; Robert Gunning; B.A Taylor. 2013. p. 67-83 (Developments in Mathematics; Vol. 28).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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AU - Sarnak, P.

AU - Ziegler, T.

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KW - Entropy

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KW - Randomness principle

KW - Square-free flow

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Disjointness of moebius from horocycle flows

Abstract

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All Science Journal Classification (ASJC) codes

Keywords

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