AI 中文总结
研究非齐次泊松对关联及其弱形式与均匀分布，通过建立结论、构造序列及证明不同参数关系，揭示弱非齐次PPC的特性及不同参数下的独立性。
AI 中文摘要
本文研究非齐次泊松对关联（PPC）、其弱形式及均匀分布。我们证明弱非齐次PPC并不意味着非齐次PPC。此外，构造了满足弱非齐次PPC但不满足均匀分布的序列，这与齐次情形形成鲜明对比。最后，证明对于不同的γ₁,γ₂ ∈(0,1/2]，弱γ₁ - PPC不意味着弱γ₂ - PPC。
英文摘要
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.
CommentsRevised version with updated references and minor corrections
