Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative

Sh A. Makhmutov; M. S. Makhmutova

doi:10.1007/s10958-020-05169-2

Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative

Sh A. Makhmutov^*, M. S. Makhmutova

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Pages (from-to)	420-427
Number of pages	8
Journal	Journal of Mathematical Sciences
Volume	252
Issue number	3
DOIs	https://doi.org/10.1007/s10958-020-05169-2
Publication status	Published - Jan 2021

Keywords

30D30, 30D35
Nevanlinna characteristics
Riemann zeta-function
meromorphic function
spherical derivative

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-020-05169-2

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title = "Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative",

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).",

keywords = "30D30, 30D35, Nevanlinna characteristics, Riemann zeta-function, meromorphic function, spherical derivative",

author = "Makhmutov, {Sh A.} and Makhmutova, {M. S.}",

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doi = "10.1007/s10958-020-05169-2",

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T1 - Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative

AU - Makhmutov, Sh A.

AU - Makhmutova, M. S.

PY - 2021/1

Y1 - 2021/1

N2 - 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).

AB - 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).

KW - 30D30, 30D35

KW - Nevanlinna characteristics

KW - Riemann zeta-function

KW - meromorphic function

KW - spherical derivative

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JF - Journal of Mathematical Sciences

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ER -

Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative

Abstract

Keywords

ASJC Scopus subject areas

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