On Joint Universality of the Riemann Zeta-Function

A theorem is obtained on the approximation of a collection of analytic functions in short intervals by a collection of shifts of the Riemann zeta-function $(\zeta(s+a_1\tau),\dots,\zeta(s+a_r\tau))$, where $a_1,\dots, a_r$ are algebraic numbers linearly independent over the field of rational numbers.