Meromorphic functions sharing three values with a derivative
type: Item
instance of: scholarly article
title: Meromorphic functions sharing three values with a derivative
zbMATH Open document ID: 0763.30011
DOI: 10.1007/BF03323115
author: Wilhelm Schwick
author: Günter Frank
published in: Results in Mathematics
publication date: 1993-04-01T00:00:00Z
review text: The following result is proved: Theorem. Let \(f\) be a meromorphic and nonconstant function and \(f^{(k)}\) its \(k\)-th derivative (\(k\in\mathbb{N}\) is a fixed number). If \(f\) and \(f^{(k)}\) do not take three (pairwise distinct) complex values then \(f\equiv f^{(k)}\). This theorem generalizes the analogous proposition of \textit{E. Mues} and \textit{N. Steinmetz} [Manuscr. Math. 29, 195-206 (1979; Zbl 0416.30028)] devoted to the case \(k=1\). The result is obtained due to traditional technics used in the value distribution theory of meromorphic functions (Nevanlinna theory).
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30B10
zbMATH DE Number: 147377
zbMATH Keywords: meromorphic functions
zbMATH Keywords: derivatives
zbMATH Keywords: Nevanlinna characteristics
reviewed by: Sergei V. Rogosin
MaRDI profile type: Publication
cites work: Meromorphic Functions That Share Four Values
cites work: Q5723337
cites work: Q3995409
cites work: Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen
full work available at URL: https://doi.org/10.1007/bf03323115
OpenAlex ID: W2059678731
description: scientific article; zbMATH DE number 147377