Metric Poissonian pair correlationa and additive energy
Abstract
In this article we prove that if the additive energy of a strictly increasing sequence (an) of natural numbers is less than N3/( N)C for some C≥13.155, then (\anα\) has Poissonian pair correlation for almost all α∈R. This provides a lower bound for the exponent C in the additive energy bound established by Bloom and Walker[3].
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