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2022 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. Advance Publication 1-16 (2022). 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. Advance Publication 1 - 16, 2022.


Published: 2022
First available in Project Euclid: 17 August 2022

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 © 2022 The Mathematical Society of the Republic of China


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