MEROMORPHIC FUNCTIONS WITH SLOW GROWTH OF NEVANLINNA CHARACTERISTICS AND RAPID GROWTH OF SPHERICAL DERIVATIVE

摘要

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).