Duke Mathematical Journal

The Möbius function and distal flows

Jianya Liu and Peter Sarnak

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Abstract

We prove that the Möbius function is linearly disjoint from an analytic skew product on the 2 -torus. These flows are distal and can be irregular in the sense that their ergodic averages need not exist for all points. The previous cases for which such disjointness has been proved are all regular. We also establish the linear disjointness of the Möbius function from various distal homogeneous flows.

Article information

Source
Duke Math. J., Volume 164, Number 7 (2015), 1353-1399.

Dates
Received: 27 June 2013
Revised: 28 June 2014
First available in Project Euclid: 14 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1431608070

Digital Object Identifier
doi:10.1215/00127094-2916213

Mathematical Reviews number (MathSciNet)
MR3347317

Zentralblatt MATH identifier
1383.11094

Subjects
Primary: 11L03: Trigonometric and exponential sums, general
Secondary: 37A45: Relations with number theory and harmonic analysis [See also 11Kxx] 11N37: Asymptotic results on arithmetic functions

Keywords
the Möbius function distal flow affine linear map skew product nilmanifold

Citation

Liu, Jianya; Sarnak, Peter. The Möbius function and distal flows. Duke Math. J. 164 (2015), no. 7, 1353--1399. doi:10.1215/00127094-2916213. https://projecteuclid.org/euclid.dmj/1431608070


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