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August, 2021 The Discrete Case of the Mixed Joint Universality for a Class of Certain Partial Zeta-functions
Roma Kačinskaitė, Kohji Matsumoto
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Taiwanese J. Math. 25(4): 647-663 (August, 2021). DOI: 10.11650/tjm/210201

Abstract

We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of Matsumoto zeta-functions $\varphi_h(s)$ and a collection of periodic Hurwitz zeta-functions $\zeta(s,\alpha;\mathfrak{B})$ under the condition that the common difference of arithmetical progression $h \gt 0$ is such that $\exp \big\{ \frac{2\pi}{h} \big\}$ is a rational number and parameter $\alpha$ is a transcendental number.

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Roma Kačinskaitė. Kohji Matsumoto. "The Discrete Case of the Mixed Joint Universality for a Class of Certain Partial Zeta-functions." Taiwanese J. Math. 25 (4) 647 - 663, August, 2021. https://doi.org/10.11650/tjm/210201

Information

Received: 15 July 2020; Accepted: 1 February 2021; Published: August, 2021
First available in Project Euclid: 24 February 2021

Digital Object Identifier: 10.11650/tjm/210201

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

Keywords: approximation , discrete shift , Euler products , Matsumoto zeta-function , periodic Hurwitz zeta-function , Universality , value distribution

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 4 • August, 2021
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