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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 1, 2002, pp. 265–272
DOI: 10.4171/ZAA/1078

Published online: 2002-03-31

Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen

Tomohiko Sato[1]

(1) Osaka University, Japan

It is well known that, when $f(z)$ is an entire function of order $\rho$ and $\rho > \infty$, then the limit lim sup$_{r \rightarrow \infty} \frac{T(r,f')}{T(r,f)}$ is finite as $r \rightarrow \infty$ through all values or outside a set $E$ of finite measure. But for $\rho = \infty$, Hayman has shown that the assertion does not hold by constructing an entire function $f(z)$ and an exceptional set $E$ of even infinite measure. In this paper, we will further extend his result to the case where $f(z)$ is an algebroid function of order $\rho = \infty$.

Keywords: Growth of characteristic functions, meromorphic functions and their derivatives, algebroid functions (in complex analysis)

Sato Tomohiko: Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen. Z. Anal. Anwend. 21 (2002), 265-272. doi: 10.4171/ZAA/1078