## Duke Mathematical Journal

### The Möbius function and distal flows

#### 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
Revised: 28 June 2014
First available in Project Euclid: 14 May 2015

https://projecteuclid.org/euclid.dmj/1431608070

Digital Object Identifier
doi:10.1215/00127094-2916213

Mathematical Reviews number (MathSciNet)
MR3347317

Zentralblatt MATH identifier
1383.11094

#### 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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