加权同时逼近下Jarnik恒等式的几何证明
A geometric proof of Jarnik's identity in the setting of weighted simultaneous approximation
摘要：
Jarnik的身份起着重要作用，在经典的同时逼近两个实数。O. German [2]给出了一个推广，其中等式必须用两个不等式代替。他的方法属于经典的数的几何。本文的目的是提供一种替代方法的基础上仔细检查某些连续的极小函数，源于参数数的几何，一种方法，已经成功地用于推广Jarnik的身份，以更高的维度在经典的设置在[3]和[7]。
英文摘要：
Jarnik's identity plays a major role in classical simultaneous approximation to two real numbers. O. German [2] has shown a generalization to the weighted setting in which the identity has to be replaced by two inequalities. His methods belong to classical geometry of numbers. The aim of this paper is to provide an alternative approach based on a careful examination of certain successive minima functions that stem from parametric geometry of numbers, a method that has already been successfully employed to generalize Jarnik's identity to higher dimensions in the classical setup in [3] and [7].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
