On the growth of the logarithmic derivative. (English) Zbl 1013.30018

Let \(f\) be a meromorphic function on \(\mathbb{C}\) with \(f(0)=1\). A. Gol’dberg and V. Grinshtein [Math. Notes 19, 320-323 (1976; Zbl 0338.30020)] sharpened the lemma of logarithmic derivative in Nevanlinna theory as follows: \[ m\left(r,\frac{f'}{f}\right)\leq \log^+\frac{\rho T(\rho,f)}{r(\rho-r)}+ c, \] where \(\rho>r\), \(c\leq 5.8501\). In this paper, the author proved \(c\leq 5.3078\).
Reviewer: Pei-Chu Hu (Jinan)


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


Zbl 0338.30020
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