Xu, Hongyan; Zhan, Tang-Sen On the existence of \(T\)-direction and Nevanlinna direction of \(K\)-quasi-meromorphic mappings dealing with multiple values. (English) Zbl 1189.30075 Bull. Malays. Math. Sci. Soc. (2) 33, No. 2, 281-294 (2010). 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. Cited in 1 Document MSC: 30D60 Quasi-analytic and other classes of functions of one complex variable Keywords:quasi-meromorphic mapping; Nevanlinna direction; \(T\)-direction PDFBibTeX XMLCite \textit{H. Xu} and \textit{T.-S. Zhan}, Bull. Malays. Math. Sci. Soc. (2) 33, No. 2, 281--294 (2010; Zbl 1189.30075) Full Text: EuDML Link