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Mat. Zametki, 1976, Volume 19, Issue 4, Pages 525–530 (Mi mz7770)  

The logarithmic derivative of a meromorphic function

A. A. Gol'dberg, V. A. Grinshtein

L'vov State University

Abstract: A well-known lemma on the logarithmic derivative for a function $f(z)$, $f(0)=1$ ($0<r<\rho<R$), meromorphic in $\{|z|<R\le\infty\}$ is proved in the following form:
$$ m(r,\frac{f'}f)<ln+\{\frac{T(\rho,f)}r\frac\rho{\rho-r}\}+5,8501. $$

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

Full text: PDF file (395 kB)

English version:
Mathematical Notes, 1976, 19:4, 320–323

Bibliographic databases:

UDC: 517.5
Received: 09.04.1975

Citation: A. A. Gol'dberg, V. A. Grinshtein, “The logarithmic derivative of a meromorphic function”, Mat. Zametki, 19:4 (1976), 525–530; Math. Notes, 19:4 (1976), 320–323

Citation in format AMSBIB
\Bibitem{GolGri76}
\by A.~A.~Gol'dberg, V.~A.~Grinshtein
\paper The logarithmic derivative of a~meromorphic function
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 4
\pages 525--530
\mathnet{http://mi.mathnet.ru/mz7770}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=402047}
\zmath{https://zbmath.org/?q=an:0338.30020|0337.30021}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 4
\pages 320--323
\crossref{https://doi.org/10.1007/BF01156790}


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