The Nevanlinna characteristic of algebroid functions and their derivatives (Q1607618)

Let \(f\) be a meromorphic function in \(\mathbb{C}\), then one knows that \[ \limsup_{r\to \infty\atop r\notin E}{T(r,f') \over T(r,f)}\leq\begin{cases} 1 \text{ if }f\text{ is entire}\\ 2\text{ if }f\text{ is meromorphic}\end{cases} \] where \(E\subset\mathbb{R}_+\) is of finite linear measure. If the order \(\rho\) of growth of \(f\) is finite then \(E=\emptyset\). Hayman constructed in the case \(\rho =\infty\) an example such that \(E\) is not empty. In this paper the author extends this construction to the case of algebroid functions of \(\rho=\infty\).