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Inverse problem of the theory of the distribution of values for meromorphic functions of finite order. (Russian) Zbl 0598.30046

The main result of the paper is the following. Let \(\{a_ j\}\) be a finite or countable subset of the extended complex plane \({\bar {\mathbb{C}}}\) and let \(\{\delta_ j\}\) be a sequence of numbers which satisfy the following conditions: \[ (i)\quad 0<\delta_ j<1,\quad (ii)\quad \sum \delta_ j<2,\quad (iii)\quad \sum \delta_ j^{1/3}<\infty. \] Then there exists a meromorphic function f of finite order such that (i) \(\delta (a_ j,f)=\delta_ j\) for every \(a_ j\in \{a_ j\}\), (ii) \(\delta (a,f)=0\) for every \(a\not\in \{a_ j\}\). Here \(\delta\) (a,f) denotes the defect in the sense of R. Nevanlinna.
Reviewer: I.V.Ostrovskij

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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