A counter-example for polynomial version of Sarnak's conjecture
Dynamical Systems
2021-05-21 v4 Number Theory
Abstract
We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the M\"obius function is linearly disjoint from subsequences along polynomials of deterministic sequences realized in minimal systems. Our example is in the class of Toeplitz systems, which are minimal.
Keywords
Cite
@article{arxiv.2002.12421,
title = {A counter-example for polynomial version of Sarnak's conjecture},
author = {Zhengxing Lian and Ruxi Shi},
journal= {arXiv preprint arXiv:2002.12421},
year = {2021}
}
Comments
Final version. To appear in Adv. Math