An algebroid function and its derivative
type: Item
instance of: scholarly article
title: An algebroid function and its derivative
zbMATH Open document ID: 1178.30038
author: Liang Meili
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-06-10T00:00:00Z
review text: Let some of the functions \[ A_v(z),\;A_{v-1}(z),\dots,A_0(z) \] be transcendental entire functions. Then the relation \[ A_v(z)W^v+A_{v-1} (z)W^{v-1}+\cdots+A)1(z) W+A_0(z)=0 \] defines a \(v\)-valued transcendental algebroid function \(W\) on the complex plane. The author takes for granted that the reader of his paper is familiar with Nevanlinna's value distribution theory. Using these results, the author proves, for example, the following relation for the characteristic functions \(T(r,W)\) and \(T(r,W')\) of \(W\) and its derivative \(W'\): Theorem 3.2. If \(\infty\not\in\{W(0)\}\), then there exists a positive number \(r_0\) such that, for \(\lambda>1\) and \(r>r_0\), \[ T(r,W')<A\frac{\lambda v}{\lambda-1}T(\lambda r,W)\quad\text{ and }\quad T (r,W)<B\frac {\lambda v}{\lambda-1}\log\frac{e\lambda}{\lambda-1}T (\lambda r,W') \] with positive absolute constants \(A\) and \(B\). As a corollary he gets that \(W\) and \(W'\) have the same lower order.
reviewed by: Rolf Wallisser
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 5563859
zbMATH Keywords: growth of algebroid functions and their derivatives
zbMATH Keywords: Nevanlinna theory for algebroid functions
zbMATH Keywords: characteristic function
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.03.014
OpenAlex ID: W2009358140
cites work: Q5723337
cites work: Q4274978
cites work: Q3317367
DOI: 10.1016/J.JMAA.2009.03.014
description: scientific article; zbMATH DE number 5563859