论文标题
数字几何形状出现的图
A graph arising in the Geometry of Numbers
论文作者
论文摘要
数字的参数几何形状允许通过相关连续的最小函数的组合图可视化实数集合的同时近似属性。通过对这些图的研究，可以猜测同时近似的经典指数之间的几种不平等。特别是所谓的常规图非常重要，因为它为其中一些不平等的极端案例提供了极为重要的。本文的目的是在加权同时近似的情况下定义和构建常规图的类似物。
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among classical exponents of simultaneous approximation can be guessed by a study of these graphs; in particular the so called regular graph is of major importance as it provides an extremal case for some of these inequalities. The aim of this paper is to define and construct an analogue of the regular graph in the case of weighted simultaneous approximation.
