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

Mathematics

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 (US)
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 - Dec 1 2024

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2024.128621

Cite this

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abstract = "In 2017 Tao proposed a variant Sarnak's M{\"o}bius 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.",

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Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

Abstract

All Science Journal Classification (ASJC) codes

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