Some difference results on Hayman conjecture and uniqueness

Document Type : Research Paper

Authors

Nanchang university, Department of mathematics

Abstract

In this paper, we show that for any finite order entire function
$f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no
nonzero finite Picard exceptional value for all nonnegative integers
$n, s$ satisfying $ngeq 3$, which can be viewed as a different
result on Hayman conjecture. We also obtain some
uniqueness theorems for difference polynomials of entire functions
sharing one common value.

Keywords

Main Subjects


Volume 38, Issue 4 - Serial Number 4
December 2012
Pages 1007-1020
  • Receive Date: 06 April 2011
  • Revise Date: 31 May 2011
  • Accept Date: 31 May 2011
  • First Publish Date: 15 December 2012