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Pair correlation of sequences
$(\lbrace a_n \alpha \rbrace)_{n \in {\mathbb N}}$ with maximal additive energy
Published online by Cambridge University Press: 06 September 2018
Abstract
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 2 , March 2020 , pp. 287 - 293
- Copyright
- Copyright © Cambridge Philosophical Society 2018
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