Universality of composite functions of periodic zeta functions
Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1631-1646
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In the paper, we prove the universality, in the sense of Voronin, for some classes of composite functions $F(\zeta(s;\mathfrak a))$, where the function $\zeta(s;\mathfrak a)$ is defined by a Dirichlet series with periodic
multiplicative coefficients. We also study the universality of functions of the form $F(\zeta(s;\mathfrak a_1),\dots,\zeta(s;\mathfrak a_r))$. For example, it follows from general theorems that every linear combination of derivatives of the function $\zeta(s;\mathfrak a)$ and every linear combination of the functions
$\zeta(s;\mathfrak a_1),\dots,\zeta(s;\mathfrak a_r)$ are universal.
Bibliography: 18 titles.
Keywords:
support of a measure, periodic zeta function, limit theorem, the space of analytic functions, universality.
@article{SM_2012_203_11_a5,
author = {A. Laurin\v{c}ikas},
title = {Universality of composite functions of periodic zeta functions},
journal = {Sbornik. Mathematics},
pages = {1631--1646},
publisher = {mathdoc},
volume = {203},
number = {11},
year = {2012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2012_203_11_a5/}
}
A. Laurinčikas. Universality of composite functions of periodic zeta functions. Sbornik. Mathematics, Tome 203 (2012) no. 11, pp. 1631-1646. http://geodesic.mathdoc.fr/item/SM_2012_203_11_a5/