论文标题
复杂平面的独特距离
Distinct distances in the complex plane
论文作者
论文摘要
我们证明，如果$ p $是$ \ mathbb {c}^2 $中的一组$ n $点，那么$ p $ nose coption conding $ω（n^{1-ε}）$复杂距离或$ p $都包含在带有坡度$ \ pm pm i $的行中。如果发生后者，则$ P $中的每对点具有复杂的距离0。
We prove that if $P$ is a set of $n$ points in $\mathbb{C}^2$, then either the points in $P$ determine $Ω(n^{1-ε})$ complex distances, or $P$ is contained in a line with slope $\pm i$. If the latter occurs then each pair of points in $P$ have complex distance 0.
