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Zbl 0643.30021
Hayman, W.K.; Miles, Joseph
On the growth of a meromorphic function and its derivatives. (English)
[J] Complex Variables, Theory Appl. 12, No.1-4, 245-260 (1989). ISSN 0278-1077; ISSN 1563-5066/e

The relative rates of growth of a function F meromorphic in the complex plane and its qth derivative $F\sp{(q)}$ are studied via the Nevanlinna characteristics $T(r,F)$ and $T(r,F\sp{(q)})$. It is shown that $$ \liminf T(r,F)/T(r,F\sp{(q)})\le 3e $$ for all meromorphic functions. A lower bound on the size of the set $\{r>1:$ $T(r,F)/T(r,F\sp{(q)})\le 3eK\}$ for $K>1$ is obtained. The upper bounds established for $T(r,F)/T(r,F')$ justify in a weakened form an old conjecture of Nevanlinna.
[W.K.Hayman]

MSC 2000:: *30D35 Distribution of values (one complex variable)

Keywords: Nevanlinna characteristics

Cited in: Zbl 0754.30024 Zbl 0703.30029

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