Geodesic
Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 128-134

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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 $\zeta(z)$.
Keywords: meromorphic function, spherical derivative, Nevanlinna characteristics, Riemann zeta-function. 
@article{INTO_2018_153_a8,
     author = {Sh. A. Makhmutov and M. S. Makhmutova},
     title = {Meromorphic {Functions} with {Slow} {Growth} of {Nevanlinna} {Characteristics} and {Rapid} {Growth} of {Spherical} {Derivative}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {128--134},
     publisher = {mathdoc},
     volume = {153},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_153_a8/}
}
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Sh. A. Makhmutov; M. S. Makhmutova. Meromorphic Functions with Slow Growth of Nevanlinna Characteristics and Rapid Growth of Spherical Derivative. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 128-134. http://geodesic.mathdoc.fr/item/INTO_2018_153_a8/