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 Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 352–369 (Mi izv1807)

In the structure of exceptional sets of entire curves

V. P. Petrenko

Abstract: Let $\vec G(z)=\{g_1(z),…,g_p(z)\}$ 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.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 335–352

Bibliographic databases:

UDC: 517.53
MSC: Primary 30A70; Secondary 30A66, 30A96

Citation: V. P. Petrenko, “In the structure of exceptional sets of entire curves”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 352–369; Math. USSR-Izv., 11:2 (1977), 335–352

Citation in format AMSBIB
\Bibitem{Pet77} \by V.~P.~Petrenko \paper In the structure of exceptional sets of entire curves \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1977 \vol 41 \issue 2 \pages 352--369 \mathnet{http://mi.mathnet.ru/izv1807} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=477052} \zmath{https://zbmath.org/?q=an:0366.32004|0378.32003} \transl \jour Math. USSR-Izv. \yr 1977 \vol 11 \issue 2 \pages 335--352 \crossref{https://doi.org/10.1070/IM1977v011n02ABEH001720}