The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (189 KB) | Metadata | Table of Contents | ZAA summary
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