Metric discrepancy results for geometric progressions perturbed by irrational rotations
Metric discrepancy results for geometric progressions perturbed by irrational rotations
复制标题
受无理旋转扰动的几何级数的公制差异结果
DOI：
10.1007/s10474-019-01003-7
复制
发表时间：
2020
影响因子：
0.9
通讯作者：
Tanabe Y.
中科院分区：
文献类型：
--
作者：
Fukuyama K.;Mori S.;Tanabe Y.
对于几乎每一个x，都知道序列是模1均匀分布的。收敛速度敏感地依赖于的代数性质。在这篇文章中，我们证明了如果我们通过加入无理旋转来扰动序列，这种依赖性就消失了。其速度与均匀分布的独立随机变量序列的速度相同。
Forand for almost everyx, it is known that the sequenceis uniformly distributed modulo 1. The speed of convergence sensitively depends on the algebraic nature of. In this paper we prove that such dependence vanishes if we perturb the sequence by adding the irrational rotation. The speed becomes identical with that of the sequence of uniformly distributed independent random variables.