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On the growth of meromorphic functions of infinite order

  • Walter Bergweiler
  • Heinrich Bock
Article

Abstract

Letf be a meromorphic function of infinite order,T(r, f) its Nevanlinna (or Ahlfors-Shimizu) characteristic, andM(r, f) its maximum modulus. It is proved that
$$\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{rT'(r,f)}} \leqslant \pi and\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{T(r,f)\psi (log T(r,f))}} = 0$$
. if ϕ (x)/x is non-decreasing, ϕ′(x)<-√ϕ(x) and ∝ dx/ϕ(x) < ∞.

Keywords

Entire Function Meromorphic Function Absolute Constant Maximum Modulus Infinite Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 1994

Authors and Affiliations

  1. 1.Lehrstuhl II für MathematikRWTH AachenAachenGermany

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