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This article is cited in 7 scientific papers (total in 7 papers)
On the Hurwitz Zeta Functions with Algebraic Irrational Parameter
A. Balčiūnas, A. Dubickas, A. Laurinčikas Institute of Mathematics, Vilnius University
Abstract:
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.
Received: 24.01.2018 Revised: 19.09.2018
Citation:
A. Balčiūnas, A. Dubickas, A. Laurinčikas, “On the Hurwitz Zeta Functions with Algebraic Irrational Parameter”, Mat. Zametki, 105:2 (2019), 179–186; Math. Notes, 105:2 (2019), 173–179
Linking options:
https://www.mathnet.ru/eng/mzm11940https://doi.org/10.4213/mzm11940 https://www.mathnet.ru/eng/mzm/v105/i2/p179
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Abstract page: | 326 | Full-text PDF : | 30 | References: | 50 | First page: | 37 |
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