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Matematicheskie Zametki, 2019, Volume 105, Issue 2, Pages 179–186
DOI: https://doi.org/10.4213/mzm11940
(Mi mzm11940)
 

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
Full-text PDF (456 kB) Citations (7)
References:
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.
Funding agency Grant number
ESF - European Social Fund 09.3.3-LMT-K-712-01-0037
The work of the second- and third-named authors was supported by the European Social Fund Agency. Measure “Development of Competences of Scientists, Other Researchers and Students through Practical Research Activities”. Activity “Improvement of researchers' qualification by implementing world-class R&D projects” under grant 09.3.3-LMT-K-712-01-0037.
Received: 24.01.2018
Revised: 19.09.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 2, Pages 173–179
DOI: https://doi.org/10.1134/S0001434619010218
Bibliographic databases:
Document Type: Article
UDC: 517
PACS: УДК511
Language: Russian
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
Citation in format AMSBIB
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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