In the structure of exceptional sets of entire curves
Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 335-352.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
@article{IM2_1977_11_2_a6,
     author = {V. P. Petrenko},
     title = {In the structure of exceptional sets of entire curves},
     journal = {Izvestiya. Mathematics },
     pages = {335--352},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a6/}
}
TY  - JOUR
AU  - V. P. Petrenko
TI  - In the structure of exceptional sets of entire curves
JO  - Izvestiya. Mathematics 
PY  - 1977
SP  - 335
EP  - 352
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a6/
LA  - en
ID  - IM2_1977_11_2_a6
ER  - 
%0 Journal Article
%A V. P. Petrenko
%T In the structure of exceptional sets of entire curves
%J Izvestiya. Mathematics 
%D 1977
%P 335-352
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a6/
%G en
%F IM2_1977_11_2_a6
V. P. Petrenko. In the structure of exceptional sets of entire curves. Izvestiya. Mathematics , Tome 11 (1977) no. 2, pp. 335-352. http://geodesic.mathdoc.fr/item/IM2_1977_11_2_a6/

[1] Weyl H., Meromorphic functions and analytic curves, Princeton, 1943 | MR

[2] Ahlfors L., “The theory of meromorphic curves”, Acta Soc. Sci. Fenn., III:4 (1941), 1–31 | MR

[3] Cartan H., “Sur les zéros des combinaisons linéaires de $p$ fonctions holomorphes données”, Mathematica, 7 (1933), 5–33

[4] Goldberg A. A., “Nekotorye voprosy teorii raspredeleniya znachenii”, Dopolnenie k kn.: G. Vittikh, Noveishie issledovaniya po odnoznachnym analiticheskim funktsiyam, Fizmatgiz, M., 1960 | MR

[5] Petrenko V. P., “Rost kvazikonformnykh tselykh krivykh”, Dokl. AN SSSR, 216:5 (1974), 982–985 | MR | Zbl

[6] Petrenko V. P., “O roste tselykh krivykh nizhnego poryadka $\lambda\leqslant1$”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 20, Kharkov, 1974, 134–140 | MR

[7] Nevanlinna R., Odnoznachnye analiticheskie funktsii, Gostekhizdat, M., L., 1941 | MR

[8] Petrenko V. P., Khussain M., “O roste tselykh krivykh”, Izvestiya AN SSSR. Seriya matem., 37 (1973), 466–477 | MR | Zbl

[9] Kheiman U. K., Meromorfnye funktsii, Mir, M., 1966 | MR

[10] Lamzina T. B., Issledovanie mnozhestv tochek priblizheniya dlya meromorfnykh funktsii i tselykh krivykh, Dissertatsiya, Kharkov, 1975 | Zbl

[11] Derkach V. S., “O svyazi mezhdu velichinoi otkloneniya i velichinoi defekta v smysle Zh. Valirona dlya $p$-mernykh $Q$-kvazikonformnykh tselykh krivykh”, Metricheskie voprosy teorii funktsii i otobrazhenii, no. 7, Kiev, 1975, 36–61