# 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.

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Main Subjects

### History

• Receive Date: 06 April 2011
• Revise Date: 31 May 2011
• Accept Date: 31 May 2011