Distribution modulo 1 and universality of the Hurwitz zeta-function

In the paper, a discrete universality theorem for the Hurwitz zeta-function ζ(s,α)ζ(s,α) on the approximation of analytic functions by shifts ζ(s+iτ,α)ζ(s+iτ,α) when τ   takes values from the set {kβh:k=0,1,…} with fixed 0<β<10<β<1 and h>0h>0 is obtained. For its proof, the uniform distribution modulo 1 is applied.