On Joint Discrete Universality of the Riemann Zeta-Function in Short Intervals

In the paper, we prove that the set of discrete shifts of the Riemann zeta-function (zeta(s + 2 pi ia(1)k), ... , zeta(s + 2 pi ia(r)k)), k is an element of N, approximating analytic non vanishing functions f(1)(s), ... , f(r)(s) defined on {s E C : 1/2 < Res < 1} has a positive density in the interval [N, N + M] with M = o(N), N -> infinity, with real algebraic numbers a(1), ... , a(r) linearly independent over Q. A similar result is obtained for shifts of certain absolutely convergent Dirichlet series.