论文标题
Sarnak的Möbius脱节，用于具有奇异频谱和莫比乌斯流的动态系统
Sarnak's Möbius disjointness for dynamical systems with singular spectrum and dissection of Möbius flow
论文作者
论文摘要
结果表明，Sarnak的Möbius正交性猜想是针对紧凑的度量动力学系统实现的，每种不变的度量都具有奇异的光谱。这是通过首先建立乔拉（Chowla）猜想的特殊情况来实现的，该猜想在Möbius函数与其正方形之间具有相关性。然后对W. Veech进行计算，然后使用“度量之间的亲和力”（或所谓的“ Hellinger方法”）的参数完成了证明。我们进一步提出了一个未发表的Veech定理，这与我们的主要结果密切相关。该定理断言，如果为了闭合Möbius函数偏移的dirac度量的任何概率措施，则第一个投影是在其Pinsker代数的矫形器中，然后SarnakMöbius的偏见构想构想。除其他后果外，我们还获得了一个简单的证据，证明了{ä} ki-Radziwiłl-tao的定理和matom {ä} ki-radziwiłl的定理，涉及liouville函数的两个命令的相关性。
It is shown that Sarnak's Möbius orthogonality conjecture is fulfilled for the compact metric dynamical systems for which every invariant measure has singular spectra. This is accomplished by first establishing a special case of Chowla conjecture which gives a correlation between the Möbius function and its square. Then a computation of W. Veech, followed by an argument using the notion of `affinity between measures', (or the so-called `Hellinger method'), completes the proof. We further present an unpublished theorem of Veech which is closely related to our main result. This theorem asserts, if for any probability measure in the closure of the Cesaro averages of the Dirac measure on the shift of the Möbius function, the first projection is in the orthocomplement of its Pinsker algebra then Sarnak Möbius disjointness conjecture holds. Among other consequences, we obtain a simple proof of Matom{ä}ki-Radziwiłl-Tao's theorem and Matom{ä}ki-Radziwiłl's theorem on the correlations of order two of the Liouville function.
