Geodesic
On the Hurwitz Zeta Functions with Algebraic Irrational Parameter
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 179-186.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is well known that the Hurwitz zeta function $\zeta(s,\alpha)$ with rational or transcendental parameter $\alpha$ is universal in the sense of Voronin, i.e., a wide class of analytic functions can be approximated by the shifts $\zeta(s+i\tau,\alpha)$, $\tau\in \mathbb R$. The case of algebraic irrational $\alpha$ is still an open problem. It is proved that there exists a nonempty closed set of analytic functions that can be approximated by shifts $\zeta(s+i\tau,\alpha)$ with algebraic irrational $\alpha$.
Keywords: algebraic irrational number, Hurwitz zeta function, limit theorem, universality. 
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A. Balčiūnas; A. Dubickas; A. Laurinčikas. On the Hurwitz Zeta Functions with Algebraic Irrational Parameter. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 179-186. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a1/

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