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 -