Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution

Zhiqin Tang; Qing-Long Zhou

Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution

Number Theory 2026-07-12 v1 Probability

Authors: Zhiqin Tang , Qing-Long Zhou

Abstract

This paper investigates inhomogeneous Poissonian pair correlation (PPC), its weak form, and equidistribution. We establish that weak inhomogeneous PPC does not imply inhomogeneous PPC. Furthermore, we construct a sequence satisfying weak inhomogeneous PPC that fails to be equidistributed, which stands in sharp contrast to the homogeneous case. Finally, we prove that for distinct $\gamma_1, \gamma_2 \in (0, \frac{1}{2}]$ , weak $\gamma_1$ -PPC does not imply weak $\gamma_2$ -PPC, showing that different inhomogeneous parameters give rise to mutually independent notions of weak inhomogeneous PPC.

Keywords

Poissonian pair correlation inhomogeneous PPC equidistribution number theory

Cite

@article{arxiv.2607.10773,
  title  = {Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution},
  author = {Zhiqin Tang and Qing-Long Zhou},
  journal= {arXiv preprint arXiv:2607.10773},
  year   = {2026}
}