On the Hurwitz Zeta Functions with Algebraic Irrational Parameter

Abstract

is well known that the Hurwitz zeta function ζ(s, α) with rational or transcendental parameter α is universal in the sense of Voronin, i.e., a wide class of analytic functions can be approximated by the shifts ζ(s + iτ, α), τ ∈ ℝ. The case of algebraic irrational α is still an open problem. It is proved that there exists a nonempty closed set of analytic functions that can be approximated by shifts ζ(s + iτ, α) with algebraic irrational α.