Riemann surface of the Riemann zeta function

In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\text{adyn}$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\text{b}=\{b_n{\}}_{n=1}^{\mathrm{\infty }}$ and $\text{z}=\{z_n{\}}_{n=1}^{\mathrm{\infty }}$. When $\text{b}=\{1{\}}_{n=1}^{\mathrm{\infty }}$ and $\text{z}=\{\frac{1}{n}{\}}_{n=1}^{\mathrm{\infty }}$ one gets the usual Riemann zeta function. Our goal in this paper is to study the meromorphic continuation of $\zeta (\text{b},\text{z},s)$ as a function of the triple $(\text{a},\text{z},s)$. Minor corrections, to appear in the Journal of Mathematical Analysis and Applications.