Abstract
Meromorphic functions with a given growth of a spherical derivative on the complex plane are described in terms of the relative location of a-points of functions. The result obtained allows one to construct an example of a meromorphic function in ℂ with a slow growth of Nevanlinna characteristics and arbitrary growth of the spherical derivative. In addition, based on the universality property of the Riemann zeta-function, we estimate the growth of the spherical derivative of ζ(z).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 153, Complex Analysis, 2018.
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Makhmutov, S.A., Makhmutova, M.S. Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative. J Math Sci 252, 420–427 (2021). https://doi.org/10.1007/s10958-020-05169-2
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DOI: https://doi.org/10.1007/s10958-020-05169-2