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Lithuanian Mathematical Journal

, Volume 59, Issue 1, pp 81–95 | Cite as

Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function

  • Renata MacaitienėEmail author
  • Darius Šiaučiūnas
Article
  • 25 Downloads

Abstract

We prove that every collection of analytic functions (f1(s), . . . , fr(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions (ζ(s + iγκh, α1),  … , ζ(s + iγκh, αr)), h > 0, where 0 < γ1 ≤ γ2 ≤ … are the imaginary parts of nontrivial zeros of the Riemann zeta-function ζ(s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over ℚ of the set {log(m + αj) : m ∈ 0, j = 1,  … , r}.

Keywords

Hurwitz zeta-function joint universality Montgomery pair correlation conjecture Riemann zeta-function weak convergence 

MSC

11M06 11M41 

Notes

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

Authors and Affiliations

  1. 1.Research Institute, Šiauliai UniversityŠiauliaiLithuania
  2. 2.Faculty of Business and TechnologiesŠiauliai State CollegeŠiauliaiLithuania
  3. 3.Department of Computer SciencesŠiauliai UniversityŠiauliaiLithuania

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