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

Author:

HE XIAOGUANGORCID,WANG KEORCID

Abstract

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].

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference16 articles.

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4. [12] Sarnak, P. , Three Lectures on the Möbius Function, Randomness and Dynamics, IAS Lecture Notes, 2009; available online at https://www.math.ias.edu/files/wam/2011/PSMobius.pdf.

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