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Two Results Related to the Universality of Zeta-Functions with Periodic Coefficients

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Abstract

In the paper, we give two results on the investigation of mixed joint universality property of the zeta-functions with periodic coefficients, i.e., we study the joint functional independence and denseness for the collections consisting of periodic zeta- and periodic Hurwitz zeta-functions. We show some generalizations as well.

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References

  1. Bagchi, B.: The Statistical Behaviour and Universality Properties of the Riemann Zeta-Function and Other Allied Dirichlet Series. Thesis, Indian Statistical Institute, Calcutta (1981)

  2. Hilbert, D.: Mathematische probleme. Nachr. Konigl. Ges. Wiss. Gott. Mat. Phys. Kl. 1900, 253–297 (1900)

    MATH  Google Scholar 

  3. Javtokas, A., Laurinčikas, A.: On the periodic Hurwitz zeta-function. Hardy-Ramanujan J. 29, 18–36 (2006)

    MathSciNet  MATH  Google Scholar 

  4. Kačinskaitė, R., Laurinčikas, A.: The joint distribution of periodic zeta-functions. Stud. Sci. Math. Hung. 48(2), 257–279 (2011)

    MathSciNet  MATH  Google Scholar 

  5. Laurinčikas, A.: Limit Theorems for the Riemann Zeta-Function. Kluwer Academic Publisher, Dordrecht (1996)

    Book  Google Scholar 

  6. Laurinčikas, A.: The joint universality for periodic Hurwitz zeta-functions. Analysis (Munich) 26(3), 419–428 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Laurinčikas, A.: Functional independence of periodic Hurwitz zeta-functions. Math. Notes. 83(1), 65–71 (2008). [Math. Zametki 83(1), 69–78 (2008) (in Russian)]

    Article  MathSciNet  Google Scholar 

  8. Laurinčikas, A.: Joint universality of zeta-functions with periodic coefficients. Izv. Ross. Akad. Nauk Ser. Mat. 74(3), 79–102 (2010). [(in Russian) Izv. Math. 74(3), 515–539 (2010)]

    Article  MathSciNet  Google Scholar 

  9. Laurinčikas, A., Macaitienė, R.: On the joint universality of periodic zeta-functions. Math. Notes 85, 51–60 (2009)

    Article  MathSciNet  Google Scholar 

  10. Laurinčikas, A., Šiaučiūnas, D.: Remarks on the universality of the periodic zeta-function. Math. Notes 80(3–4), 711–722 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Mergelyan, S.N.: Uniform approximations to functions of complex variable. Usp. Mat. Nauk 7, 31–122 (1952)

    MathSciNet  MATH  Google Scholar 

  12. Mishou, H.: The joint value-distribution of the Riemann zeta-function and Hurwitz zeta-function. Lith. Math. J. 47(1), 32–47 (2007)

    Article  MathSciNet  Google Scholar 

  13. Schnee, W.: Die Funktionalgleichung der Zetafunktion und der Dirichletschen Reiben mit periodishen Koeffizienten. Math. Z. 31, 378–390 (1930)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  15. Voronin, S.M.: On differential independence of \( \zeta \)-functions. Dokl. Akad. Nauk SSSR 209(6), 1264–1266 (1973). (in Russian)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Informatics, Vytautas Magnus University, Vileikos 8, 44404, Kaunas, Lithuania

    Roma Kačinskaitė & Brigita Kazlauskaitė

Authors
  1. Roma Kačinskaitė
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  2. Brigita Kazlauskaitė
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Correspondence to Roma Kačinskaitė.

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In honour of Professor A. Laurinčikas on his 70th birthday.

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Kačinskaitė, R., Kazlauskaitė, B. Two Results Related to the Universality of Zeta-Functions with Periodic Coefficients. Results Math 73, 95 (2018). https://doi.org/10.1007/s00025-018-0856-z

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  • DOI: https://doi.org/10.1007/s00025-018-0856-z

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