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Joint value distribution for zeta functions in disjoint strips

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Abstract

In this paper we investigate joint functional distribution for a set of zeta functions which belong to the Selberg class. Especially we establish a similar property to the joint universality theorem for the zeta functions.

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References

  1. Bagchi, B.: The statistical behavior and universality properties of the Riemann zeta-function and other allied Dirichlet series, PhD Thesis, Indian Statistical Institute, Calcutta (1981)

  2. Bagchi, B.: A joint universality theorem for Dirichlet \(L\)-functions. Math. Z. 181(3), 319–334 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bauer, H.: The value distribution of Artin \(L\)-series and zeros of zeta-functions. J. Number Theory 98(2), 254–279 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bohr, H.: Über das Verhalten von \(\zeta (s)\) in der Halbebene \(\sigma >1\), Nachr. Akad. Wiss. Göttingen II Math. Phys. Kl., pp. 409–428 (1911)

  5. Bohr, H., Courant, R.: Neue Anwendungen der Theorie der Diophantischen auf die Riemannsche Zetafunktion. J. Reine Angew. Math. 144, 249–274 (1914)

    MATH  Google Scholar 

  6. Gonek, S.M.: Analytic properties of zeta and \(L\)-functions. Thesis, University of Michigan (1979)

  7. Kaczorowski, J., Laurinčikas, A., Steuding, J.: On the value distribution of shifts of universal Dirichlet series. Monatsh. Math. 147(4), 309–317 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Karatsuba, A.A., Voronin, S.M.: The Riemann zeta function. de Gruyter, New York (1992)

    Book  MATH  Google Scholar 

  9. Laurinčikas, A.: Limit theorems for the Riemann zeta-function. Mathematics and its Applications, vol. 352. Kluwer, Dordrecht (1996)

  10. Laurinčikas, A., Matsumoto, K.: The joint universality of twisted automorphic \(L\)-functions. J. Math. Soc. Japan 56, 923–939 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nagoshi, H.: Discrepancy of Hecke eigenvalues and joint universality of automorphic \(L\)-functions. Preprint

  12. Nagoshi, H., Steuding, J.: Universality for \(L\)-functions in the Selberg class. Lithuanian Math. J. 50(3), 293–311 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Selberg, A.: Old and new conjectures and results about a class of Dirichlet series. In: Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), pp. 367–385. Univ. Salerno (1992)

  14. Steuding, J.: Value-distribution of \(L\)-functions. In: Lecture Notes in Mathematics, vol. 1877. Springer, Berlin (2007)

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

  16. Voronin, S.M.: Analytic properties of Dirichlet generating functions of arithmetic objects. Math. Notes 24(6), 966–969 (1978)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The author would like to thank Professor Hirofumi Nagoshi and Takashi Nakamura for their useful advice. Also the author would like to express his appreciation to the referee for the comments and the suggestion.

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Authors and Affiliations

  1. Ube National College of Technology, 2-14-1 Tokiwadai, Ube City, Yamaguchi, 755-8555, Japan

    Hidehiko Mishou

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  1. Hidehiko Mishou
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Correspondence to Hidehiko Mishou.

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Communicated by J. Schoißengeier.

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Mishou, H. Joint value distribution for zeta functions in disjoint strips. Monatsh Math 169, 219–247 (2013). https://doi.org/10.1007/s00605-012-0449-y

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  • DOI: https://doi.org/10.1007/s00605-012-0449-y

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