Rouché定理与有理函数几何
Rouché's Theorem and the Geometry of Rational Functions
摘要：
本文利用Rouché定理和对数导数的算术性质，建立了关于有理函数的零点、极点和临界点几何性质的若干新结果.包括亚历山大和沃尔什的结果的改进，从一个给定的零或极点的有理函数到最近的临界点的距离。
英文摘要：
In this note, we use Rouché's theorem and the pleasant properties of the arithmetic of the logarithmic derivative to establish several new results regarding the geometry of the zeros, poles, and critical points of a rational function. Included is an improvement on a result by Alexander and Walsh regarding the distance from a given zero or pole of a rational function to the nearest critical point.
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。
