论文标题
树设置中的ERDOS-FALCONER距离问题
The Erdos-Falconer distance problem in the tree setting
论文作者
论文摘要
Guth，Iosevich，Ou和Wang（2019）最近在Falconer距离问题上的突破指出，如果$ a $ a $的Hausdorff尺寸大于$ \ frac {5} {4} $ set $ natus $ natus $ natus $ natus $ natus $ natus $ nature，则为紧凑型设置$ a \ subset \ subset \ subset \ mathbb {r}^2 $，如果$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $。在最近的一篇论文中，墨菲，彼得里迪斯，帕姆，鲁德纳夫和史蒂文斯（2022）证明了这种结果的主要现场版本，即，对于$ e \ subset \ subset \ mathbb {f} _p} _p^2 $ with $ | e | e | e | e | e | e | e | e | e | e | e | $ CP $。本文的主要目的是在固定树的非常通用的结构中提供扩展，这是受到OU和Taylor（2021）的最新工作的启发。
The recent breakthrough of Guth, Iosevich, Ou, and Wang (2019) on the Falconer distance problem states that for a compact set $A\subset \mathbb{R}^2$, if the Hausdorff dimension of $A$ is greater than $\frac{5}{4}$, then the distance set $Δ(A)$ has positive Lebesgue measure. In a very recent paper, Murphy, Petridis, Pham, Rudnev, and Stevens (2022) proved the prime field version of this result, namely, for $E\subset\mathbb{F}_p^2$ with $|E|\gg p^{5/4}$, there exist many points $x\in E$ such that the number of distinct distances from $x$ is at least $cp$. The main purpose of this paper is to provide extensions in a very general structure of pinned trees, which is inspired by the recent work due to Ou and Taylor (2021).
