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