**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