Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function. II

Let 0 < γ1 < ⋯ ≤ γk ≤ ⋯ be the sequence of imaginary parts of nontrivial zeros of the Riemann zetafunction. In [R. Macaitienė and D. Šiaučiūnas, Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function, Lith. Math. J., 59(1):81–95, 2019] a joint universality theorem on the approximation of analytic functions by shifts of the Hurwitz zeta-functions ζ(s + ihγk, α1), …, ζ(s + ihγk, αr) has been obtained. In the paper, we prove universality theorems for the compositions F(ζ(s + ihγk, α1), …, ζ(s + ihγk, αr)) for some classes of operators in the r-dimensional space of analytic functions.