Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.737 ) Pub Date : 2018-09-06 , DOI: 10.1017/s030500411800066x
GERHARD LARCHER; WOLFGANG STOCKINGER

We show for sequences $\left(a_{n}\right)_{n \in \mathbb N}$ of distinct positive integers with maximal order of additive energy, that the sequence $\left(\left\{a_{n} \alpha\right\}\right)_{n \in \mathbb N}$ does not have Poissonian pair correlations for any α. This result essentially sharpens a result obtained by J. Bourgain on this topic.

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