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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1978 Volume 42, Issue 5, Pages 1021–1049 (Mi im1918)

This article is cited in 3 papers

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.

UDC: 511.6+517.56

MSC: Primary 30D35; Secondary 30D20, 30G30

Received: 19.04.1976


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

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