Pair correlation of sequences with maximal additive energy
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 re...
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2020-03, Vol.168 (2), p.287-293 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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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| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S030500411800066X |