论文标题
Möbius随机定律和无限排名一号地图
Möbius random law and infinite rank-one maps
论文作者
论文摘要
我们证明，萨尔纳克（Sarnak）的猜想适用于任何无限度量的符号排名第一地图。我们进一步扩展了Bourgain-Sarnak的结果，该结果称Möbius函数对于厄戈迪克定理来说是一个很好的重量，以映射作用于$σ$ - 罚款空间的效果。我们还通过确定有一类地图来讨论和扩展波尔加因定理，其中Möbius的偏置属性为任何连续的有界函数所具有的。我们的证明使我们能够获得有关莫比乌斯（Möbius）偏见的一条地图的莫比乌斯（Möbius）定理的扩展，以及对这一事实的简单且独立的证据。
We prove that Sarnak's conjecture holds for any infinite measure symbolic rank-one map. We further extended Bourgain-Sarnak's result, which says that the Möbius function is a good weight for the ergodic theorem, to maps acting on $σ$-finite measure spaces. We also discuss and extend Bourgain's theorem by establishing that there is a class of maps for which the Möbius disjointness property holds for any continuous bounded function. Our proof allows us to obtain an extension of Bourgain's theorem on Möbius disjointness for bounded rank one maps and a simple and self-contained proof of this fact.
