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On zeros of normal functions. (English) Zbl 1017.30039

The paper concerns the zeros of normal functions, little normal functions and functions of uniformly bounded characteristic. Necessary conditions are obtained for zero sets of these functions. The main results are as follows.
(i) If \(f\) is normal then the zeros of \(f\) satisfy \(\prod^N_{n=1} \frac 1{|z_n|} = O(N^{{\|f\|}^2/2})\), as \(N \to \infty\);
(ii) if \(f\) is little normal then \(\sum ^N_{n=1} \log \frac 1{|z_n|} = o (\log N)\), as \(N \to \infty\);
(iii) similar conditions are given for zeros of functions of uniformly bounded characteristic. It is a question whether these condtions are sharp or not.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D45 Normal functions of one complex variable, normal families
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