Remark on a result of Bourgain on poissonian pair correlation
Abstract
We show for a class of sequences (an)n≥ 1 of distinct positive integers, that for no α the sequence (\an α \)n ≥ 1 does have Poissonian pair correlation. This class contains for example all strictly increasing integer sequences with positive upper density. This result motivates us to state a certain conjecture on Poissonian pair correlation which would be a significantly stronger version of a result of Jean Bourgain.
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