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. 
@article{MZM_2019_105_2_a1,
     author = {A. Bal\v{c}i\={u}nas and A. Dubickas and A. Laurin\v{c}ikas},
     title = {On the {Hurwitz} {Zeta} {Functions} with {Algebraic} {Irrational} {Parameter}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {179--186},
     publisher = {mathdoc},
     volume = {105},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a1/}
}
TY  - JOUR
AU  - A. Balčiūnas
AU  - A. Dubickas
AU  - A. Laurinčikas
TI  - On the Hurwitz Zeta Functions with Algebraic Irrational Parameter
JO  - Matematičeskie zametki
PY  - 2019
SP  - 179
EP  - 186
VL  - 105
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a1/
LA  - ru
ID  - MZM_2019_105_2_a1
ER  - 
%0 Journal Article
%A A. Balčiūnas
%A A. Dubickas
%A A. Laurinčikas
%T On the Hurwitz Zeta Functions with Algebraic Irrational Parameter
%J Matematičeskie zametki
%D 2019
%P 179-186
%V 105
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a1/
%G ru
%F MZM_2019_105_2_a1
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/