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Monatshefte für Mathematik

, Volume 165, Issue 3–4, pp 433–446 | Cite as

On universality for linear combinations of L-functions

  • Takashi Nakamura
  • Łukasz Pańkowski
Open Access
Article

Abstract

In the present paper, we consider the universality property in the Voronin sense for certain combinations of L-functions with general Dirichlet series as coefficients. In addition, we present some interesting examples of zeta and L-functions which can be expressed in this form. More precisely, we obtain the universality theorem for zeta functions associated to certain arithmetic functions, zeta functions associated to symmetric matrices and Euler–Zagier double zeta and L-functions.

Keywords

Hybrid universality Linear combination of L-functions Zeros of L-functions Zeta functions associated to arithmetic functions Zeta functions associated to symmetric matrices Euler–Zagier double zeta-function 

Mathematics Subject Classification (2000)

11M32 11M35 11M41 

Notes

Acknowledgments

We would like to thank the anonymous referee for very useful comments and remarks.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyTokyo University of Science NodaChibaJapan
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznanPoland

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