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 $0<\alpha <1,\alpha \ne \frac{1}{2}$ then $f(s)$ may be uniformly approximated arbitrarily closely by $\zeta (1+iT+i\delta s,\alpha )$ on $K$ for some $T,\delta >0$, where $\zeta (s,\alpha )$ 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.

16 pages

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Cited by in corpus (2)

• Voronin universality on the abscissa of absolute convergence
• Joint universality on the half plane of absolute convergence