Pair correlation of sequences (\lbrace a_n α\rbrace)_{n ∈ ℕ} with maximal order of additive energy

2018/02/07 by Larcher, Gerhard, Stockinger, Wolfgang
#11K06 #11K31 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.02901

Abstract

We show for sequences (a_n)_{n ∈ ℕ} of distinct positive integers with maximal order of additive energy, that the sequence (\a_n α\)_{n ∈ 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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