Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

Amir Algom; Zhiren Wang

doi:10.1016/j.jmaa.2024.128621

Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

Amir Algom, Zhiren Wang

Department of Mathematics, Physics and Computer Science (Oranim Campus)

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

Abstract

In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system (X,T), [Formula presneted] for every f∈C(X) and every x∈X. We construct examples showing that this o(1) can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture.

Original language	English
Article number	128621
Journal	Journal of Mathematical Analysis and Applications
Volume	540
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2024.128621
State	Published - 1 Dec 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Möbius disjointness
Topological dynamics
Zero topological entropy

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2024.128621

Cite this

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AB - In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system (X,T), [Formula presneted] for every f∈C(X) and every x∈X. We construct examples showing that this o(1) can go to zero arbitrarily slowly. Nonetheless, all of our examples satisfy the conjecture.

KW - Möbius disjointness

KW - Topological dynamics

KW - Zero topological entropy

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Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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