A discrete version of the Mishou theorem. II

Abstract

In 2007, H. Mishou obtained a joint universality theorem for the Riemann zetafunction ζ(s) and the Hurwitz zeta-function ζ(s, α) with transcendental parameter α. The theorem states that a pair of analytic functions can be simultaneously approximated by the shifts ζ(s + iτ ) and ζ(s + iτ, α), τ ∈ R. In 2015, E. Buivydas and the author established a version of this theorem in which the approximation is performed by the discrete shifts ζ(s + ikh) and ζ(s + ikh, α), h > 0, k = 0, 1, 2.... In the present study, we prove joint universality for the functions ζ(s) and ζ(s, α) in the sense of approximation of a pair of analytic functions by the shifts ζ(s + ik^βh) and ζ(s + ik^βh, α) with fixed 0 < β < 1.