The value distribution of entire functions of finite order
type: Item
instance of: scholarly article
title: The value distribution of entire functions of finite order
zbMATH Open document ID: 0691.30021
author: Jianyong Qiao
published in: Kodai Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The author proves the following theorem: Let \(f(z)\) be an entire function and let \(\{w_ n\}\) be an unbounded sequence. Suppose that for some positive integer \(m\) \[ \underline{\lim}_{r\to \infty}\frac{T(r,f)}{r^ m}=0. \] Assume that there exists some \(\varepsilon >0\) such that all the roots of \( f(z)=w_ n\) \((n=1,2,...) \) belong to the following set \[ \cup^{m-1}_{k=0}\{z;\frac{2k}{m}\pi +\varepsilon <\arg z<\frac{2k+1}{m}\pi -\varepsilon \}. \] Then \(f(z)\) is a polynomial.
reviewed by: Fred Gross
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 4130730
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039107
OpenAlex ID: W2074837410
cites work: Q3207265
cites work: Q5616324
cites work: On meromorphic functions with regions free of poles and zeros
cites work: On the value distribution of entire functions of order less than one
cites work: Distribution of values of entire functions of lower order less than one
cites work: On entire functions of infinite order with radially distributed zeros
cites work: On the solution of the functional equation $f\circ g(z)=F(z)$. III.
DOI: 10.2996/KMJ/1138039107
description: scientific article; zbMATH DE number 4130730