This research demonstrates Poissonian pair correlation in sequences with low additive energy, indicating a critical exponent bound.
In this article we prove that if the additive energy of a strictly increasing sequence (aₙ) of natural numbers is less than N³/(log N)C for some C≥13.155, then (ₙα\) has Poissonian pair correlation for almost all α. This provides a lower bound for the exponent C in the additive energy bound established by Bloom and Walker[3].
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Bera et al. (2025) studied this question.
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