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arXiv · 1303.4957

The M\"obius function and distal flows

Jianya Liu·Peter Sarnak
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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 M\"{o}bius from various distal homogeneous flows.

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Jianya Liu, Peter Sarnak. 2013-03-20. The M\"obius function and distal flows. https://doi.org/10.1215/00127094-2916213

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