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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