论文标题
Waring问题的密度版本
A Density version of Waring's problem
论文作者
论文摘要
在本文中，我们研究了Waring问题的密度版本。我们证明，$ k $ th-th-powers的正密度子集构成了$ o（k^2）$的渐近添加剂，前提是该集合的相对较低密度大于$（1- \ Mathcal {z} _k} _k^{ - 1}/2}/2}/2）/2） $ \ MATHCAL {Z} _K>每$ K $和$ \ lim_ {k \ rightArrow \ infty} \ Mathcal {z} _K = 1 $。
In this paper, we study a density version of Waring's problem. We prove that a positive density subset of $k$th-powers forms an asymptotic additive basis of order $O(k^2)$ provided that the relative lower density of the set is greater than $(1 - \mathcal{Z}_k^{-1}/2)^{1/k}$, where $\mathcal{Z}_k$ is certain constant depending on $k$ for which it holds that $\mathcal{Z}_k > 1$ for every $k$ and $\lim_{k \rightarrow \infty} \mathcal{Z}_k = 1$.
