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

Access to Document

10.1016/j.jmaa.2024.128621

Cite this

@article{d07893a8dcb747a288cf41195ff4a68c,

title = "Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture",

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.",

keywords = "M{\"o}bius disjointness, Topological dynamics, Zero topological entropy",

author = "Amir Algom and Zhiren Wang",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = dec,

day = "1",

doi = "10.1016/j.jmaa.2024.128621",

language = "English",

volume = "540",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

AU - Algom, Amir

AU - Wang, Zhiren

PY - 2024/12/1

Y1 - 2024/12/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=85196479522&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2024.128621

DO - 10.1016/j.jmaa.2024.128621

M3 - Article

AN - SCOPUS:85196479522

SN - 0022-247X

VL - 540

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 128621

ER -

Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this