Composite meromorphic functions and growth of the spherical derivative. (English) Zbl 0990.30021
Let \(f\) be a transcendental meromorphic function, \(g\) a transcendental entire function. It is shown in this paper that if \(f\) takes every value \(c\in\widehat C:=C\cup\{\infty\}\) at least twice and \(h\) is a meromorphic function satisfying
\[
\limsup_{r\to\infty} {r\mu(r,g)\over 1+\max_{|t-r|\leq K/\mu(r,g)} t\mu(r,h)}= \infty
\]
for all \(K>0\) where \(\mu(r,w):= \max_{|z|= r} {|w'(z)|\over|t|w(t)|^2}\). Then there exists an unbounded sequence \(\{\zeta_n\}\) such that \(f(g(\zeta_n))= h(\zeta_n)\).
Reviewer: He Yuzan (Beijing)
MSC:
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 30D30 | Meromorphic functions of one complex variable (general theory) |
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