## Disjointness of M\"{o}bius from asymptotically periodic functions. (arXiv:1810.07360v1 [math.NT])

In this paper, we introduce asymptotically periodic functions and study these functions from the point of view of operator algebras and dynamical systems. We show that the M\"{o}bius function is disjoint from any strongly asymptotically periodic functions. As a consequence, Sarnak's M\"{o}bius Disjointness Conjecture holds for all countable compact spaces. Whenever Sarnak's conjecture holds, we show that the M\"{o}bius function is disjoint from all asymptotically periodic functions.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 In this paper, we introduce asymptotically periodic functions and study these functions from the point of view of operator algebras and dynamical systems. We show that the M\"{o}bius function is disjoint from any strongly asymptotically periodic functions. As a consequence, Sarnak's M\"{o}bius Disjointness Conjecture holds for all countable compact spaces. Whenever Sarnak's conjecture holds, we show that the M\"{o}bius function is disjoint from all asymptotically periodic functions.
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