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On the Functional Equation P(F)=Q(G)

  • Ha Huy Khoai 
  • Yang C. C. 
Part of the Advances in Complex Analysis and Its Applications book series (ACAA, volume 3)

Abstract

We prove that for a generic pair (P, Q) of polynomials P of degree n and Q of degree m, where m, n are satisfying some conditions, P(f)=Q(g) for meromorphic functions f,g implies f=const, g=const. We also give another proof of the statement saying that a generic polynomial of degree at least 5 is a uniqueness polynomial for meromorphic functions.

Key words and phrases

functional equation uniqueness polynomial meromorphic function unique range set 

Mathematics Subject Classification 2000

32H20 30D35 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ha Huy Khoai 
    • 1
  • Yang C. C. 
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Department of MathematicsHong Kong University of Science and TechnologyKowloonHong Kong, China

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