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A NOTE ON MÖBIUS DISJOINTNESS FOR SKEW PRODUCTS ON A CIRCLE AND A NILMANIFOLD

Part of: Multiplicative number theory Exponential sums and character sums

Published online by Cambridge University Press:  04 October 2022

XIAOGUANG HE Open the ORCID record for XIAOGUANG HE [Opens in a new window]  and
KE WANG Open the ORCID record for KE WANG [Opens in a new window]
XIAOGUANG HE*
Affiliation:
College of Mathematical Sciences, Sichuan University, Chengdu, Sichuan 610016, PR China
KE WANG
Affiliation:
Data Science Institute, Shandong University, Jinan, Shandong 250100, PR China e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

Let $\mathbb {T}$ be the unit circle and ${\Gamma \backslash G}$ the $3$ -dimensional Heisenberg nilmanifold. We consider the skew products on $\mathbb {T} \times {\Gamma \backslash G}$ and prove that the Möbius function is linearly disjoint from these skew products which improves the recent result of Huang, Liu and Wang [‘Möbius disjointness for skew products on a circle and a nilmanifold’, Discrete Contin. Dyn. Syst. 41(8) (2021), 3531–3553].

Keywords

Möbius functiondistal flowskew productnilmanifoldmeasure complexity

MSC classification

Secondary: 11L03: Trigonometric and exponential sums, general 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 3 , June 2023 , pp. 471 - 482
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is supported by the National Postdoctoral Innovative Talents Support Program (Grant No. BX20190227), the Fundamental Research Funds for the Central Universities, SCU (No. 2021SCU12109) and the National Natural Science Foundation of China (Grant No. 12101427).

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