On joint universality of the Riemann zeta-function and Hurwitz zeta-functions

We construct classes of composite functions of the Riemann zeta-function and Hurwitz zeta function with transcendental parameter which are universal in the sense that their shifts uniformly on compact subsets of some region approximate any analytic function. For example, the functions c1ζ(s)+c2ζ(s,α),c1,c2∈C∖{0}, eζ(s)+ζ(s,α) and sin(ζ(s)+ζ(s,α)) are universal.