Disjointness of M\"{o}bius from asymptotically periodic functions
Number Theory
2022-07-29 v8
Abstract
We investigate Sarnak's M\"obius Disjointness Conjecture through asymptotically periodic functions. It is shown that Sarnak's conjecture for rigid dynamical systems is equivalent to the disjointness of M\"obius from asymptotically periodic functions. We give sufficient conditions and a partial answer to the later one. As an application, we show that Sarnak's conjecture holds for a class of rigid dynamical systems, which improves an earlier result of Kanigowski-Lema{\'{n}}czyk-Radziwi{\l}{\l}.
Keywords
Cite
@article{arxiv.1810.07360,
title = {Disjointness of M\"{o}bius from asymptotically periodic functions},
author = {Fei Wei},
journal= {arXiv preprint arXiv:1810.07360},
year = {2022}
}
Comments
47 pages, this paper was recently published in Pure and Applied Mathematics Quarterly