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

Sh. A. Makhmutov ; M. S. Makhmutova

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 128-134.

Résumé

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 $\zeta(z)$.

Détail

Keywords: meromorphic function, spherical derivative, Nevanlinna characteristics, Riemann zeta-function.

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