In the paper, a joint universality theorem for the Riemann zeta-function and a collection of periodic Hurwitz zeta-functions on approximation of analytic functions is obtained.

No abstract

The periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the function ζ(s; a), for some sequences a of coefficients, is universal in the sense that its shifts ζ(s + iτ ; a), τ ∈ R, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the function ζ(s; a) is obtained.

No abstract

In the paper, a weighted theorem on the approximation of a wide class of analytic functions by shifts ζ(s + ikαh; a), k ∈ N, 0 < α < 1, and h > 0, of the periodic zeta-function ζ(s; a) with multiplicative periodic sequence a, is obtained.