The discrete universality of the periodic Hurwitz zeta function

The periodic Hurwitz zeta function [image omitted], s=sigma+it, 01, is defined, for sigma 1, by [image omitted] and by analytic continuation elsewhere. Here {am} is a periodic sequence of complex numbers. In this paper, a discrete universality theorem for the function [image omitted] with a transcendental parameter is proved. Roughly speaking, this means that every analytic function can be approximated uniformly on compact sets by shifts [image omitted], where m is a non-negative integer and h is a fixed positive number such that [image omitted] is rational.