The möbius function and distal flows

Jianya Liu; Peter Sarnak

doi:10.1215/00127094-2916213

The möbius function and distal flows

Jianya Liu, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1353-1399
Number of pages	47
Journal	Duke Mathematical Journal
Volume	164
Issue number	7
DOIs	https://doi.org/10.1215/00127094-2916213
State	Published - 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2916213

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title = "The m{\"o}bius function and distal flows",

abstract = "We prove that the M{\"o}bius 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 M{\"o}bius function from various distal homogeneous flows.",

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AB - 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.

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The möbius function and distal flows

Abstract

All Science Journal Classification (ASJC) codes

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