On the uniqueness of entire functions
Bull. Korean Math. Soc. 2004 Vol. 41, No. 1, 109-116
Published online March 1, 2004
Huiling Qiu and Mingliang Fang
Nanjing Normal University, Nanjing Normal University
Abstract : In this paper, we study the uniqueness of entire functions and prove the following result: Let $f(z)$ and $g(z)$ be two nonconstant entire functions, $n\ge 7$ a positive integer, and let $a$ be a nonzero finite complex number. If $f^{n}(z)(f(z)-1)f'(z)$ and $g^{n}(z)(g(z)-1)g'(z)$ share $a$ CM, then $f(z)\equiv g(z)$. The result improves the theorem due to ref. [3].
Keywords : entire function, sharing value, uniqueness
MSC numbers : 30D35
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