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

2020/08/11 by Johan Andersson, Andersson, Johan
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.04709

openalex publication_date 2020/08/11 · openalex created_date 2020/08/18 · openalex updated_date 2026/07/28

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 00, 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.

Citations

• On generalized Hardy classes of Dirichlet series
• Voronin universality on the abscissa of absolute convergence

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