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

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