In the structure of exceptional sets of entire curves

V. P. Petrenko

Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 335-352

Résumé

Let $\vec G(z)=\{g_1(z),\dots,g_p(z)\}$ be a $p$-dimensional entire curve, $D(\vec G)=\{\vec a:\delta(\vec a,\vec G)>0\}$, $V(\vec G)=\{\vec a:\Delta(\vec a,\vec G)>0\}$ and $\Omega(\vec G)=\{\vec a:\beta(\vec a,\vec G)>0\}$ its sets of deficient values and set of positive deviations. This paper is devoted to an investigation of the structure of $D(\vec G)$, $V(\vec G)$ and $\Omega(\vec G)$ without any supplementary assumption that the vectors belong to a fixed admissible system. The main result shows that these sets are exceptional in a certain sense. Bibliography: 11 titles.