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Value Distribution Theory and Related Topics pp 201–207Cite as

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

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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.

Mathematics Subject Classification 2000

  • 32H20
  • 30D35

Key words and phrases

  • functional equation
  • uniqueness polynomial
  • meromorphic function
  • unique range set

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Hanoi, Vietnam

    Huy Khoai Ha

  2. Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong, China

    C. C. Yang

Authors
  1. Huy Khoai Ha
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  2. C. C. Yang
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Editor information

Editors and Affiliations

  1. National Academy of Sciences of Armenia, Yerevan, Armenia

    G. Barsegian

  2. University of Joensuu, Joensuu, Finland

    I. Laine

  3. Hong Kong University of Science and Technology, Hong Kong, China

    C. C. Yang

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© 2004 Kluwer Academic Publishers

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Ha, H.K., Yang, C.C. (2004). On the Functional Equation P(F)=Q(G). In: Barsegian, G., Laine, I., Yang, C.C. (eds) Value Distribution Theory and Related Topics. Advances in Complex Analysis and Its Applications, vol 3. Springer, Boston, MA. https://doi.org/10.1007/1-4020-7951-6_10

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  • DOI: https://doi.org/10.1007/1-4020-7951-6_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7950-4

  • Online ISBN: 978-1-4020-7951-1

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