On Mixed Joint Discrete Universality for a Class of Zeta-functions: One More Case

Abstract

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 $\varphi(s)$.