论文标题
Möbius脱节的任意缓慢衰减猜想
Arbitrarily slow decay in the Möbius disjointness conjecture
论文作者
论文摘要
Sarnak'sMöbius的莫比乌斯（Möbius）的偏见猜想断言，对于任何零熵动力学系统$（x，t）$，$ \ frac {1} {n} {n} \ sum_ {n = 1} ^n f（t ^n x）μ（t ^n x）μ（n）= o（n）= o（n）= o（n）= o（1）$ in \ in \ in \ in \ mathcal \ in \ in \ in c $ f \ in \ in \ in c $ f \ in \ in c} $ in \ in c}我们构建了示例，表明此$ O（1）$可以随意缓慢地达到零。实际上，我们的方法产生了更一般的结果，其中代替了$μ（n）$的一个人可以放置任何有界序列，以使绝对值相应序列的均值不倾向于为零。
Sarnak's Möbius disjointness conjecture asserts that for any zero entropy dynamical system $(X,T)$, $\frac{1}{N} \sum_{n=1} ^N f(T^n x) μ(n)= o(1)$ for every $f\in \mathcal{C}(X)$ and every $x\in X$. We construct examples showing that this $o(1)$ can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of $μ(n)$ one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero.
