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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)420-427
Number of pages8
JournalJournal of Mathematical Sciences
Volume252
Issue number3
DOIs
Publication statusPublished - Jan 2021
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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