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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 5, Pages 1021–1049 (Mi izv1918)  

On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order

V. I. Krutin'


Abstract: In this paper analogues of results of W. K. Hayman and V. I. Petrenko for functions meromorphic in the finite complex plane are established. The results concern $p$-dimensional entire curves $\vec G(z)=\{g_n(z)\}_1^p$ (where the $g_n(z)$ are linearly independent integral functions). We show that $\sum_{\vec a\in A}\beta^\alpha(\vec a,\vec G)$ converges for $1\ge\alpha>1/2$ and $\sum_{\vec a\in A}\delta^\alpha(\vec a,\vec G)$ converges for $\alpha>1/3$, where $\beta(\vec a,\vec G)$ is the magnitude of the positive deviation of the integral curve, $\delta(\vec a,\vec G)$ the Nevanlinna defect and $A$ an admissible system of vectors.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:2, 307–334

Bibliographic databases:

UDC: 511.6+517.56
MSC: Primary 30D35; Secondary 30D20, 30G30
Received: 19.04.1976

Citation: V. I. Krutin', “On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978), 1021–1049; Math. USSR-Izv., 13:2 (1979), 307–334

Citation in format AMSBIB
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\by V.~I.~Krutin'
\paper On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 5
\pages 1021--1049
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=513912}
\zmath{https://zbmath.org/?q=an:0431.30019|0406.30020}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 2
\pages 307--334
\crossref{https://doi.org/10.1070/IM1979v013n02ABEH002045}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JD23800006}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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