Universality of the Hurwitz zeta-function in short intervals

In the paper, we consider approximation of analytic functions by shifts zeta(s + i tau, alpha), s = sigma +it, of the Hurwitz zeta-function with transcendental parameter alpha, for tau is an element of [T, T+H], where T-27/82 <= H <= T-1/2. We obtain that the set of these shifts approximating a given analytic function on the strip 1/2 < sigma < 1 has a positive density. For the proof, a mean square estimate for zeta(sigma + it, alpha) with 1/2< sigma <= 7/12 in the interval [T, T+H] and a probabilistic limit theorem in the space of analytic functions are applied.