The Tumura-Clunie theorem in several complex variables

P. C. Hu; C. C. Yang

The Tumura-Clunie theorem in several complex variables

Authors

P. C. Hu Shandong University
C. C. Yang Shandong University

Keywords:

meromorphic function, Nevanlinna theory, Tumura-Clunie theorem.

Abstract

It is a well-known result that if a nonconstant meromorphic function

$f$ on

${\bf C}$ and its

$l$ -th derivative

$f^{(l)}$ have no zeros for some

$l\geq 2$ , then

$f$ is of the form

$f(z)=\exp(Az+B)$ or

$f(z)=(Az+B)^{-n}$ for some constants

$A$ ,

$B$ . We have extended this result to meromorphic functions of several variables, by first extending the classic Tumura-Clunie theorem for meromorphic functions of one complex variable to that of meromorphic functions of several complex variables by using Nevanlinna theory. DOI:- 10.1017/S0004972714000446

Published

2014-09-20

Issue

Vol. 90 No. 3 (2014)

Section

Articles

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