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The logarithmic derivative of a meromorphic function

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Abstract

A well-known lemma on the logarithmic derivative for a function f(z), f(0) = 1 (0 < r <ϱ<R), meromorphic in {¦z¦<R ≤ ∞ is proved in the following form:

$$m\left( {r,\frac{{f'}}{f}} \right)< \ln + \left\{ {\frac{{T(\rho ,f)}}{r}\frac{\rho }{{\rho - r}}} \right\} + 5.8501.$$

. This estimate is more exact than the one previously obtained by Kolokol'nikov and is, in a certain sense, unimprovable.

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Literature cited

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Authors and Affiliations

  1. L'vov State University, USSR

    A. A. Gol'dberg & V. A. Grinshtein

Authors
  1. A. A. Gol'dberg
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  2. V. A. Grinshtein
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Additional information

Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 525–530, April, 1976.

The authors thank A. S. Kolokol'nikov for discussing this note.

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Gol'dberg, A.A., Grinshtein, V.A. The logarithmic derivative of a meromorphic function. Mathematical Notes of the Academy of Sciences of the USSR 19, 320–323 (1976). https://doi.org/10.1007/BF01156790

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  • DOI: https://doi.org/10.1007/BF01156790

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