A new theorem shows that a small-scale additive energy estimate plus a weighted large-gap sum implies metric Poissonian pair correlation, yielding the property for quantitatively convex and real polynomial sequences.
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Metric Poissonian pair correlation for real sequences and energy estimates
A new theorem shows that a small-scale additive energy estimate plus a weighted large-gap sum implies metric Poissonian pair correlation, yielding the property for quantitatively convex and real polynomial sequences.