Pair correlation of sequences ({anα})n∈N with maximal additive energy

We show for sequences (a(n))(n is an element of N) of distinct positive integers with maximal order of additive energy, that the sequence (a(n)alpha)(n is an element of N) does not have Poissonian pair correlations for any alpha. This result essentially sharpens a result obtained by J. Bourgain on this topic.