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arXiv · 2001.10536

Value distribution theory and Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre"

Athanase Papadopoulos
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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.

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Athanase Papadopoulos. 2020-01-28. Value distribution theory and Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre". https://arxiv.org/abs/2001.10536

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