Universality of the Hurwitz zeta-function on the half plane of absolute convergence

Abstract

Let $K$ be a compact set with connected complement on the half-plane Re$(s)>0$, and let $f$ be a continuous function on $K$ which is analytic in its interior. We prove that for any parameter $0<α<1, α\neq \frac 1 2$ then $f(s)$ may be uniformly approximated arbitrarily closely by $ζ(1+iT+iδs,α)$ on $K$ for some $T,δ>0$, where $ζ(s,α)$ denote the Hurwitz zeta-function. This is the first known universality result that is also known to hold for the Hurwitz zeta-function with an algebraic irrational parameter.