Geodesic
A discrete version of the Mishou theorem. II
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 181-191.

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In 2007, H. Mishou obtained a joint universality theorem for the Riemann zeta-function $\zeta (s)$ and the Hurwitz zeta-function $\zeta (s,\alpha )$ with transcendental parameter $\alpha $. The theorem states that a pair of analytic functions can be simultaneously approximated by the shifts $\zeta (s+i\tau )$ and $\zeta (s+i\tau ,\alpha )$, $\tau \in \mathbb R$. In 2015, E. Buivydas and the author established a version of this theorem in which the approximation is performed by the discrete shifts $\zeta (s+ikh)$ and $\zeta (s+ikh,\alpha )$, $h>0$, $k=0,1,2\dots {}\kern 1pt$. In the present study, we prove joint universality for the functions $\zeta (s)$ and $\zeta (s,\alpha )$ in the sense of approximation of a pair of analytic functions by the shifts $\zeta (s+ik^\beta h)$ and $\zeta (s+ik^\beta h,\alpha )$ with fixed $0\beta 1$. 
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     author = {A. Laurin\v{c}ikas},
     title = {A discrete version of the {Mishou} theorem. {II}},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a13/}
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A. Laurinčikas. A discrete version of the Mishou theorem. II. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 181-191. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a13/

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