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Mathematical Notes

, Volume 105, Issue 1–2, pp 173–179 | Cite as

On the Hurwitz Zeta Functions with Algebraic Irrational Parameter

  • A. BalčiūnasEmail author
  • A. DubickasEmail author
  • A. LaurinčikasEmail author
Article
  • 7 Downloads

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.

Keywords

algebraic irrational number Hurwitz zeta function limit theorem universality 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of MathematicsVilnius UniversityVilniusLithuania

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