Metric Poissonian pair correlationa and additive energy

Tanmoy Bera; E. Malavika

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arXiv · 2506.15274

Metric Poissonian pair correlationa and additive energy

Tanmoy Bera·E. Malavika

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Abstract

In this article we prove that for a strictly increasing sequence $(a_n)$ of natural numbers, if the additive energy of $\{a_n:n\leq N\}$ is less than $N^3/(\log N)^C$ for some $C\geq14.71,$ then $(\{a_n\alpha\})$ has Poissonian pair correlation for almost all $\alpha\in\mathbb{R}.$ This provides a lower bound for the exponent $C$ in the additive energy bound established by Bloom and Walker [4].

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Tanmoy Bera, E. Malavika. 2025-06-18. Metric Poissonian pair correlationa and additive energy. https://arxiv.org/abs/2506.15274

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