Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CERTAIN DIFFERENCE POLYNOMIALS AND SHARED VALUES

  • Li, Xiao-Min (Department of Mathematics Ocean University of China) ;
  • Yu, Hui (Department of Mathematics Ocean University of China)
  • Received : 2017.10.13
  • Accepted : 2018.04.03
  • Published : 2018.09.30
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Abstract

Let f and g be nonconstant meromorphic (entire, respectively) functions in the complex plane such that f and g are of finite order, let a and b be nonzero complex numbers and let n be a positive integer satisfying $n{\geq}21$ ($n{\geq}12$, respectively). We show that if the difference polynomials $f^n(z)+af(z+{\eta})$ and $g^n(z)+ag(z+{\eta})$ share b CM, and if f and g share 0 and ${\infty}$ CM, where ${\eta}{\neq}0$ is a complex number, then f and g are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from.

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Acknowledgement

Supported by : NSFC, NSF of Shandong Province

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