Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen

Abstract

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 $\rho = \infty$.