Although a generic uniformly distributed sequence has Poissonian pair correlations, only one explicit example has been found up to now. Additionally, it is even known that many classes of uniformly distributed sequences, like van der Corput sequences, Kronecker sequences and LS sequences, do not have Poissonian pair correlations. In this paper, we show that van der Corput sequences and the Kronecker sequence for the golden mean are as close to having Poissonian pair correlations as possible: they both have α-pair correlations for all $0<\alpha <1$ but not for $\alpha =1$ which corresponds to Poissonian pair correlations.

中文翻译：

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具有几乎泊松对相关的序列

虽然一个通用的均匀分布序列具有泊松对相关性，但到目前为止只发现了一个明确的例子。此外，甚至已知许多类均匀分布的序列，如 van der Corput 序列、Kronecker 序列和 LS 序列，不具有泊松对相关性。在本文中，我们展示了用于黄金均值的 van der Corput序列和 Kronecker 序列尽可能接近泊松对相关：它们都具有$0<\alpha <1$但不是为了$\alpha =1$这对应于泊松对相关。