On the growth of meromorphic functions of infinite order

  • Walter Bergweiler
  • Heinrich Bock


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) < ∞.


Entire Function Meromorphic Function Absolute Constant Maximum Modulus Infinite Order 
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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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