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A generalization of the Voronin theorem

  • Antanas LaurinčikasEmail author
  • RenataMacaitienė
  • Darius Šiaučiūnas
Article
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Abstract

The classical Voronin universality theorem asserts that a wide class of analytic functions can be approximated by shifts of the Riemann zeta-function ζ(s + iτ), τ ∈ . In the paper, we generalize this approximation for shifts ζ(s + iφ(τ)), where 𝜑(τ) has the monotonic positive derivative such that 1/𝜑′(τ) = o(τ) and φ(2τ) × maxτ ≪ t ≪ 2τ(1/φ(t)) ≪ τ as τ →∞.

Keywords

Haar measure limit theorem Mergelyan theorem Riemann zeta function universality 

MSC

11M06 

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References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Antanas Laurinčikas
    • 1
    Email author
  • RenataMacaitienė
    • 2
    • 3
  • Darius Šiaučiūnas
    • 2
    • 3
  1. 1.Institute of Mathematics, Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Research InstituteŠiauliai UniversityŠiauliaiLithuania
  3. 3.Department of Computer SciencesŠiauliai UniversityŠiauliaiLithuania

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