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This article is cited in 2 scientific papers (total in 2 papers)
On the Hurwitz Zeta-Function with Algebraic Irrational Parameter. II
A. Laurinčikas Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
Abstract:
It is known that the Hurwitz zeta-function $\zeta (s,\alpha )$ with transcendental or rational parameter $\alpha $ has a discrete universality property; i.e., the shifts $\zeta (s+ikh,\alpha )$, $k\in \mathbb N_0$, $h> 0$, approximate a wide class of analytic functions. The case of algebraic irrational $\alpha $ is a complicated open problem. In the paper, some progress in this problem is achieved. It is proved that there exists a nonempty closed set $F_{\alpha ,h}$ of analytic functions such that the functions in $F_{\alpha ,h}$ are approximated by the above shifts. Also, the case of certain compositions $\Phi (\zeta (s,\alpha ))$ is discussed.
Received: June 2, 2020 Revised: September 16, 2020 Accepted: April 22, 2021
Citation:
A. Laurinčikas, “On the Hurwitz Zeta-Function with Algebraic Irrational Parameter. II”, Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, Steklov Math. Inst., Moscow, 2021, 134–144; Proc. Steklov Inst. Math., 314 (2021), 127–137
Linking options:
https://www.mathnet.ru/eng/tm4165https://doi.org/10.4213/tm4165 https://www.mathnet.ru/eng/tm/v314/p134
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