On a Generalization of Voronin’s Theorem

Voronin’s theorem states that the Riemann zeta-function ζ(s) is universal in the sense that all analytic functions that are defined and have no zeros on the right half of the critical strip can be approximated by the shifts ζ(s + iτ), τ ∈ ℝ. Some results on the approximation by the shifts ζ(s + iϕ(τ)) with some function ϕ(τ) are also known. In this paper, it is established that an analytic function without zeros in the strip 1/2 + 1/(2α) < Res < 1 can be approximated by the shifts ζ(s + i logατ) with α > 1.