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Some questions of the Nevanlinna theory for the complex half-plane. (English) Zbl 0913.30020

The authors give variants of the logarithmic derivative lemma and of the second main theorem for the Nevanlinna characteristic functions of meromorphic functions in the complex half-plane. There are many other results as well. For example, the authors investigate the continuity of the function \(T'(r,f)\), give analogs of the potential theory theorems of Eremenko and Sodin (1991) for the half-plane. They introduce the widest class of meromorphic functions in the half-plane that have meaningfull Nevanlinna characteristic functions. The authors discuss what is \(m(r,f)\) and \(N(r,f)\) for the half-plane case.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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