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

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 $\mathbb{C}$ 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 $\zeta(z)$.