A discrete version of the Mishou theorem. II

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 + i τ ) and ζ( s + i τ, 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 β h ) and ζ( s + ik β h , α) with fixed 0 < β < 1.