Universality of the Riemann zeta-function in short intervals

By the Voronin theorem, the set of shifts of the Riemann zeta-function zeta(s+i tau), s = sigma + it, tau is an element of R, that approximate any given non-vanishing analytic function defined on {s is an element of C : 1/2 < sigma < 1} has a positive lower density. In the paper, it is proved that the same property of the above shifts remains valid in the intervals [T,T + H] with T-1/3(log T)(26/15) <= H <= T. (C) 2019 Elsevier Inc. All rights reserved.