Joint Value-Distribution of Shifts of the Riemann Zeta-Function

We prove that any complex values z 1 , … , z n can be approximated by the following integral shifts of the Riemann zeta-function ζ ( s + i d 1 τ ) , … , ζ ( s + i d n τ ) for infinitely many τ , provided d 1 , … , d n ∈ Q are distinct and positive, and s is a fixed complex number lying in the right open half of the critical strip.