论文标题
价值分布理论和teichm {ü} ller的论文“ Einfache beispiele zur wertverteilungslehre”
Value distribution theory and Teichm{ü}ller's paper "Einfache Beispiele zur Wertverteilungslehre"
论文作者
论文摘要
该调查将在第1卷中出现。 Teichm {ü} ller理论的Hendbook的VII（欧洲数学学会出版社，2020年）。这是对Teichm {ü} ller的论文“ Einfache beispiele Zur wertverteilungslehre”的评论，于1944年出版，其英语翻译出现在该卷中。与Teichm {ü} ller的论文一起，我们调查了价值分布理论的发展，从高斯开始的作品开始，从代数的基本定理到Teichm {ü} ller的工作结束。我们提到了几位数学家的基础作品，包括皮卡德，拉瓜尔，庞卡{é}，哈玛德，博雷尔，蒙特尔，维龙等，我们快速概述了尼凡克林纳及其对该理论的一些结果。
This survey will appear in Vol. VII of the Hendbook of Teichm{ü}ller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichm{ü}ller's paper "Einfache Beispiele zur Wertverteilungslehre", published in 1944, whose English translation appears in that volume. Together with Teichm{ü}ller's paper, we survey the development of value distribution theory, in the period starting from Gauss's work on the Fundamental Theorem of Algebra and ending with the work of Teichm{ü}ller. We mention the foundational work of several mathematicians, including Picard, Laguerre, Poincar{é}, Hadamard, Borel, Montel, Valiron, and others, and we give a quick overview of the various notions introduced by Nevanlinna and some of his results on that theory.
