论文标题
小组动作和$ l^2 $ - 纳尔的几何问题估计值
Group action and $L^2$-norm estimates of geometric problems
论文作者
论文摘要
在2017年，通过使用组理论方法，Bennett，Hart，Iosevich，Pakianathan和Rudnev获得了有关简单和总产品类型问题的分布的许多结果。本文的主要目的是提供一系列强大框架的新应用程序，即，我们专注于距离集的产品和商，$ l^2 $ - 方向集的$ l^2 $ norm和$ l^2 $ norm scales in差异集。
In 2017, by using the group theoretic approach, Bennett, Hart, Iosevich, Pakianathan, and Rudnev obtained a number of results on the distribution of simplices and sum-product type problems. The main purpose of this paper is to give a series of new applications of their powerful framework, namely, we focus on the product and quotient of distance sets, the $L^2$-norm of the direction set, and the $L^2$-norm of scales in difference sets.
