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Mathematics of the USSR-Izvestiya, 1977, Volume 11, Issue 2, Pages 335–352
DOI: https://doi.org/10.1070/IM1977v011n02ABEH001720
(Mi im1807)
 

In the structure of exceptional sets of entire curves

V. P. Petrenko
References:
Abstract: 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.
Received: 21.08.1975
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1977, Volume 41, Issue 2, Pages 352–369
Bibliographic databases:
UDC: 517.53
MSC: Primary 30A70; Secondary 30A66, 30A96
Language: English
Original paper language: Russian
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/im1807}
\mathscinet{http://mathscinet.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}
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  • https://doi.org/10.1070/IM1977v011n02ABEH001720
  • https://www.mathnet.ru/eng/im/v41/i2/p352
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    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:204
    Russian version PDF:56
    English version PDF:3
    References:43
    First page:1
     
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