# There is no Khintchine threshold for metric pair correlations

19 Nov 2018 Aistleitner Christoph Lachmann Thomas Technau Niclas

We consider sequences of the form $\left(a_{n} \alpha\right)_{n}$ mod 1, where $\alpha\in\left[0,1\right]$ and where $\left(a_{n}\right)_{n}$ is a strictly increasing sequence of positive integers. If the asymptotic distribution of the pair correlations of this sequence follows the Poissonian model for almost all $\alpha$ in the sense of Lebesgue measure, we say that $(a_n)_n$ has the metric pair correlation property... (read more)

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