Zhaojun Wu, Daochun Sun

On a Singular Direction of a Meromorphic Function

Abstract:
By using Ahlfors' theory of a covering surface, we establish the existence of a new singular direction for a meromorphic function $f$, namely a $T$ direction for $f$, for which the Nevanlinna characteristic function $T(r,f)$ is used as a comparison function. Then we prove that every $T$ direction is a Borel direction for meromorphic function with finite and positive regular growth order.

Keywords:
$T$ direction, Ahlfors-Shimizu characteristic function, Nevanlinna characteristic function, comparison function.

MSC 2000: 30D35, 30D30