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On the existence of \(T\)-direction and Nevanlinna direction of \(K\)-quasi-meromorphic mappings dealing with multiple values. (English) Zbl 1189.30075

Summary: By using Ahlfors’ theory of covering surfaces, we prove that for a quasi-meromorphic mapping \(f\) satisfying \[ \text{lim} \underset{r\to \infty} {\text{sup}} \frac{T(r,f)}{(\log r)^2} = +\infty, \]
there exists at least one \(T\)-direction of \(f\) dealing with multiple values. Under the same condition, we also prove that there exists at least one Nevanlinna direction of \(f\) dealing with multiple values, which is also a \(T\)-direction of \(f\) dealing with multiple values.

MSC:

30D60 Quasi-analytic and other classes of functions of one complex variable
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