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The generalized strong recurrence for non-zero rational parameters

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An Erratum to this article was published on 17 July 2012

Abstract

The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers.

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References

  1. T. Aoyama, private comunication.

  2. Bagchi B.: A joint universality theorem for Dirichlet L-functions. Math. Z. 181, 319–334 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Denjoy A.: L’hypothèse de Riemann sur la distribution des zéros de ζ(s), reliée à la théorie des probabilités. Comptes Rendus Acad. Sci. Paris 192, 656–658 (1931)

    Google Scholar 

  4. R. Garunkštis Self-approximation of Dirichlet L-functions, arXiv:1006.1507.

  5. A. Laurinčikas, Limit Theorems for the Riemann Zeta-function, Kluwer Academic Publishers, 1996.

  6. Nakamura T.: The joint universality and the generalized strong recurrence for Dirichlet L-functions. Acta Arith. 138, 357–362 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Nakamura, Some topics related to universality of L-functions with an Euler product, to appear in Analysis.

  8. Ł. Pańkowski, Some remarks on the generalized strong recurrence for L-functions, New directions in value-distribution theory of zeta and L-functions 305–315, Ber. Math., Shaker Verlag, Aachen, 2009.

  9. J. Steuding, Value Distributions of L-functions, Lecture Notes in Mathematics 1877, Springer-Verlag, 2007.

  10. E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., edited and with a preface by D. R. Heath-Brown, The Clarendon Press (Oxford University Press, New York, 1986).

  11. S. M. Voronin, Theorem on the universality of the Riemann zeta-function, Izv. Akad. Nauk. SSSR Ser. Mat. 39 (1975), 475–486 (in Russian); Math. USSR Izv. 9 (1975), 443–453.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan

    Takashi Nakamura

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  1. Takashi Nakamura
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Correspondence to Takashi Nakamura.

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Nakamura, T. The generalized strong recurrence for non-zero rational parameters. Arch. Math. 95, 549–555 (2010). https://doi.org/10.1007/s00013-010-0205-2

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  • DOI: https://doi.org/10.1007/s00013-010-0205-2

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