Abstract
We derive the following estimate for the quantity m(r,f′/tf) of the Nevanlinna theory of the distribution of values characterizing the growth of the logarithmic derivative of a meromorphic functionf(z),f(0) = 1, 0 < r < R < ∞: m(r,f′/f) < 1n+ [T(R,f)/r (R/R−r)2] + 6.0084. This estimate is more accurate than that obtained earlier by Vu Ngoyan and I. V. Ostrovskii.
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Literature cited
R. Nevanlinna, Eindeutige analitische Funktionen, Berlin (1936).
A. A. Gol'dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).
Vu Ngoyan and I. V. Ostrovskii, “On the logarithmic derivative of a meromorphic function,” Dokl. Akad. Nauk Arm. SSR,41, 272–277 (1965).
M. V. Keldysh, “On series in rational fractions,” Dokl. Akad. Nauk SSSR,94, No. 3, 377–380 (1954).
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Translated from Matematicheskie Zametki, Vol. 15, No. 5, pp. 711–718, May, 1974.
The author expresses his thanks to I. V. Ostrovskii for suggesting the topic of this paper and for his interest in my work.
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Kolokol'nikov, A.S. On the logarithmic derivative of a meromorphic function. Mathematical Notes of the Academy of Sciences of the USSR 15, 425–429 (1974). https://doi.org/10.1007/BF01152778
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DOI: https://doi.org/10.1007/BF01152778