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/(2 α ) < Res < 1 can be approximated by the shifts ζ ( s + i log α τ ) with α > 1.