Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 7 (2015), 1353-1399.
The Möbius function and distal flows
We prove that the Möbius function is linearly disjoint from an analytic skew product on the -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.
Duke Math. J., Volume 164, Number 7 (2015), 1353-1399.
Received: 27 June 2013
Revised: 28 June 2014
First available in Project Euclid: 14 May 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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