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April, 2023 On Mixed Joint Discrete Universality for a Class of Zeta-functions: One More Case
Roma Kačinskaitė, Kohji Matsumoto, Łukasz Pańkowski
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Taiwanese J. Math. 27(2): 221-236 (April, 2023). DOI: 10.11650/tjm/220804


We prove a new case of mixed discrete joint universality theorem on approximation of certain target couple of analytic functions by the shifts of a pair consisting of the function $\varphi(s)$ belonging to wide class of Matsumoto zeta-functions and the periodic Hurwitz zeta-function $\zeta(s,\alpha;\mathfrak{B})$. We work under the condition that the common difference of arithmetical progression $h > 0$ is such that $\exp \{2\pi/h\}$ is a rational number and the parameter $\alpha$ is a transcendental number. The essential difference from the result in our previous article [10] is that here we do not study the class of partial zeta-functions $\varphi_{h}(s)$, but work with the class of the original functions $\varphi(s)$.

Funding Statement

The third author was partially supported by the grant no. 2016/23/D/ST1/01149 from the National Science Centre.


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Roma Kačinskaitė. Kohji Matsumoto. Łukasz Pańkowski. "On Mixed Joint Discrete Universality for a Class of Zeta-functions: One More Case." Taiwanese J. Math. 27 (2) 221 - 236, April, 2023.


Received: 11 November 2021; Revised: 15 June 2022; Accepted: 8 August 2022; Published: April, 2023
First available in Project Euclid: 17 August 2022

MathSciNet: MR4563517
Digital Object Identifier: 10.11650/tjm/220804

Primary: 11M06 , 11M36 , 11M41 , 30E10 , 41A30

Keywords: approximation , discrete shift , Euler products , limit theorem , Matsumoto zeta-function , periodic Hurwitz zeta-function , rational number , Universality , value distribution , weak convergence

Rights: Copyright © 2023 The Mathematical Society of the Republic of China

Vol.27 • No. 2 • April, 2023
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