Joint Functional Independence of the Riemann Zeta-Function

By the Ostrowski theorem, the Riemann zeta-function zeta(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta (s)$$\end{document} does not satisfy any algebraic-differential equation. Voronin proved that the function zeta(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta (s)$$\end{document} does not satisfy algebraic-differential equation with continuous coefficients. In the paper, a joint generalization of the Voronin theorem is given, i. e., that a collection (zeta(s1),& ctdot;,zeta(sr))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\zeta (s_1), \dots , \zeta (s_r))$$\end{document} does not satisfy a certain algebraic-differential equation with continuous coefficients.