Modification of the Mishou theorem
Čebyševskij sbornik, Tome 17 (2016) no. 3, pp. 135-147
Voir la notice de l'article provenant de la source Math-Net.Ru
The Mishou theorem asserts that a pair of analytic functions from a wide class can be approximated by shifts of the Riemann zeta and Hurwitz zeta-functions $(\zeta(s+i\tau), \zeta(s+i\tau, \alpha))$ with transcendental $\alpha$, $\tau\in\mathbb{R}$, and that the set of such $\tau$ has a positive lower density. In the paper, we prove that the above set has a positive density for all but at most countably many $\varepsilon>0$, where $\varepsilon$ is the accuracy of approximation. We also obtain similar results for composite functions $F(\zeta(s),\zeta(s,\alpha))$ for some classes of operator $F$.
Bibliography: 21 titles.
Keywords:
Hurwitz zeta-function, Riemann zeta-function, space of analytic functions, universality.
@article{CHEB_2016_17_3_a9,
author = {A. Laurin\v{c}ikas and L. Me\v{s}ka},
title = {Modification of the {Mishou} theorem},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {135--147},
publisher = {mathdoc},
volume = {17},
number = {3},
year = {2016},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CHEB_2016_17_3_a9/}
}
A. Laurinčikas; L. Meška. Modification of the Mishou theorem. Čebyševskij sbornik, Tome 17 (2016) no. 3, pp. 135-147. http://geodesic.mathdoc.fr/item/CHEB_2016_17_3_a9/