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1 October 2018 Möbius disjointness for homogeneous dynamics
Ryan Peckner
Duke Math. J. 167(14): 2745-2792 (1 October 2018). DOI: 10.1215/00127094-2018-0026

Abstract

We prove Sarnak’s Möbius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if G is any such group, ΓG a lattice, and uG an Ad-unipotent element, then for every xΓ\G and every function f continuous on the 1-point compactification of Γ\G, the sequence f(xun) cannot correlate with the Möbius function on average.

Citation

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Ryan Peckner. "Möbius disjointness for homogeneous dynamics." Duke Math. J. 167 (14) 2745 - 2792, 1 October 2018. https://doi.org/10.1215/00127094-2018-0026

Information

Received: 6 November 2016; Revised: 18 April 2018; Published: 1 October 2018
First available in Project Euclid: 28 September 2018

zbMATH: 06982206
MathSciNet: MR3859364
Digital Object Identifier: 10.1215/00127094-2018-0026

Subjects:
Primary: 11N37
Secondary: 22D40

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 14 • 1 October 2018
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