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arXiv · 2607.10773

Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution

Zhiqin Tang·Qing-Long Zhou
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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 $γ_1, γ_2 \in (0, \frac{1}{2}]$, weak $γ_1$-PPC does not imply weak $γ_2$-PPC, showing that different inhomogeneous parameters give rise to mutually independent notions of weak inhomogeneous PPC.

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Zhiqin Tang, Qing-Long Zhou. 2026-07-15. Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution. https://arxiv.org/abs/2607.10773

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