TY - JOUR

T1 - Arbitrarily slow decay in the Möbius disjointness conjecture

AU - Algom, Amir

AU - Wang, Zhiren

N1 - Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

PY - 2023/9/9

Y1 - 2023/9/9

N2 - Sarnak's Möbius disjointness conjecture asserts that for any zero entropy dynamical system, for every and every. We construct examples showing that this can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of, one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. Moreover, in our construction, the choice of x depends on the sequence anbut does not.

AB - Sarnak's Möbius disjointness conjecture asserts that for any zero entropy dynamical system, for every and every. We construct examples showing that this can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of, one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. Moreover, in our construction, the choice of x depends on the sequence anbut does not.

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U2 - 10.1017/etds.2022.61

DO - 10.1017/etds.2022.61

M3 - Article

AN - SCOPUS:85169050745

SN - 0143-3857

VL - 43

SP - 2863

EP - 2880

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 9

ER -