On the pair correlations of powers of real numbers
On the pair correlations of powers of real numbers
复制标题
论实数幂的配对相关性
DOI：
10.1007/s11856-021-2130-4
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发表时间：
2019
影响因子：
1
通讯作者：
S. Baker
中科院分区：
文献类型：
--
作者：
C. Aistleitner;S. Baker
一个经典的Koksma定理指出，对于Lebesgue，几乎每x > 1序列（xn）n=1∞都是模为1的均匀分布。本文将Koksma定理推广到对相关集。更准确地说，我们证明了对于Lebesgue几乎每x > 1, (xn)n=1∞的分数部分的对相关是渐近泊松的。证明是基于鞅近似方法。
A classical theorem of Koksma states that for Lebesgue almost every x > 1 the sequence (xn)n=1∞ is uniformly distributed modulo one. In the present paper we extend Koksma’s theorem to the pair correlation setting. More precisely, we show that for Lebesgue almost every x > 1 the pair correlations of the fractional parts of (xn)n=1∞ are asymptotically Poissonian. The proof is based on a martingale approximation method.
影响因子：
0.7
作者：
Baker S
通讯作者：
Baker S