The work of Walter Bergweiler in value distribution of meromorphic functions

TL;DR

This paper discusses Walter Bergweiler's contributions to the value distribution theory of meromorphic functions, focusing on Picard theorem generalizations and the Bloch principle, with an accessible overview of Nevanlinna theory.

Contribution

It highlights Bergweiler's novel work on extending Picard's theorem to differential polynomials and applying the rescaling principle in value distribution.

Findings

Generalizations of Picard's theorem to differential polynomials

Applications of the rescaling principle (Bloch Principle)

Accessible introduction to Nevanlinna theory

Abstract

This is a colloquium talk in CAU, Kiel delivered on June 7, 2024 on the occasion of Walter Bergweiler's retirement. Walter's work on meromorphic functions consists of two parts: generalizations of Picard's theorem to differential polynomials, and the applications of the rescaling principle known as the Bloch Principle. Since the talk was aimed at the general audience, a brief introduction to Nevanlinna theory is included.