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This is a Quantitative Study study.

October 20, 2025Open Access

Metric Poissonian pair correlationa and additive energy

Key Points

If the additive energy of a strictly increasing sequence is below a certain threshold, Poissonian pair correlation occurs.
A significant result found is that the exponent C must be at least 13.155 for the additive energy condition to hold.
This research establishes a lower bound for the exponent in additive energy, building on previous work by Bloom and Walker.
The findings suggest a connection between additive energy bounds and the distribution properties of sequences in number theory.

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 C13. 155, then (\aₙα\) 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 Walker3.

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Cite This Study

Bera et al. (Wed,) studied this question.

synapsesocial.com/papers/68f6379bb481a140a36cf707 https://doi.org/https://doi.org/10.48550/arxiv.2506.15274

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