Value distribution theory and Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre"
Abstract
This survey will appear in Vol. VII of the Hendbook of Teichm{\"u}ller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre", published in 1944, whose English translation appears in that volume. Together with Teichm{\"u}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{\"u}ller. We mention the foundational work of several mathematicians, including Picard, Laguerre, Poincar{\'e}, 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.
Keywords
Cite
@article{arxiv.2001.10536,
title = {Value distribution theory and Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre"},
author = {Athanase Papadopoulos},
journal= {arXiv preprint arXiv:2001.10536},
year = {2020}
}