The Discrete Case of the Mixed Joint Universality for a Class of Certain Partial Zeta-functions

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.