Aequationes mathematicae

, Volume 63, Issue 1–2, pp 140–151 | Cite as

Growth of meromorphic solutions of some functional equations I

  • W. Bergweiler
  • K. Ishizaki
  • N. Yanagihara
Article

Summary.

We show that each transcendental meromorphic solution f(z) of the functional equation \( \sum_{j=0}^na_j(z)f(c^jz) = Q(z) \), where Q and the \( a_{j},\,j = 0, \dots, n \) are polynomials without common zeros, \( a_n(z)a_0(z) \ne 0 \) and 0 < |c| < 1, satisfies \( m(r,f) = \sigma_f(\log r)^2(1+o(1)) \) for some constant \( \sigma_f \).

Keywords. Functional equation, Value distribution theory, Growth of meromorphic function. 

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Copyright information

© Birkhäuser Verlag, Basel, 2002

Authors and Affiliations

  • W. Bergweiler
    • 1
  • K. Ishizaki
    • 2
  • N. Yanagihara
    • 3
  1. 1.Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludwig-Meyn-Str. 4, D-24098 Kiel, Germany, e-mail: bergweiler@math.uni-kiel.deGermany
  2. 2.Department of Mathematics, NIPPON Institute of Technology, 4-1 Gakuendai Miyashiro, Minamisaitama Saitama 345-8501, Japan, e-mail: ishi@nit.ac.jpJapan
  3. 3.Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Inageku, Chiba 263, Japan, e-mail: yanagi@math.s.chiba-u.ac.jpJapan

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