Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function

We prove that every collection of analytic functions (f1(s), . . . , fr(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions (ζ(s + iγκh, α1),  … , ζ(s + iγκh, αr)), h > 0, where 0 < γ1 ≤ γ2 ≤ … are the imaginary parts of nontrivial zeros of the Riemann zeta-function ζ(s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over ℚ of the set {log(m + αj) : m ∈ ℕ0, j = 1,  … , r}.