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Approximation of analytic functions by an absolutely convergent Dirichlet series

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Abstract

In the paper, an absolutely convergent Dirichlet series whose shifts approximate a wide class of analytic functions is constructed. This series is close in the mean to the Riemann zeta-function.

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References

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

  2. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968)

    MATH  Google Scholar 

  3. Gonek, S.M.: Analytic properties of zeta and \(L\)-functions. PhD Thesis, University of Michigan, Ann Arbor (1975)

  4. Ivič, A.: The Riemann Zeta-Function. The Theory of the Riemann Zeta-Function with Applications. Wiley, New York (1985)

    MATH  Google Scholar 

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

    Book  Google Scholar 

  6. Laurinčikas, A., Garunkštis, R.: The Lerch Zeta-Function. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  7. Laurinčikas, A., Meška, L.: Sharpening of the universality inequality. Math. Notes 96(5–6), 971–976 (2014)

    Article  MathSciNet  Google Scholar 

  8. Matsumoto, K.: A survey on the theory of universality for zeta and \(L\)-functions. In: Number Theory, pp. 95–144. Ser. Number Theory Appl., vol. 11. World Sci. Publ., Hackensack, New York (2015)

  9. Mauclaire, J.-L.: Universality of the Riemann zeta-function: two remarks. Ann. Univ. Sci. Budapest. Sect. Comput. 39, 311–319 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Mergelyan, S.N.: Uniform approximations to functions of a complex variable. Amer. Math. Soc. Translation 1954(101), 99 pp. (1954)

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

  12. Titchmarsh, E.C.: The Theory of Functions, 2nd edn. Oxford University Press, Oxford (1952)

  13. Voronin, S.M.: Theorem on the “universality” of the Riemann zeta-function. Math. USSR Izv. 9(3), 443–453 (1975)

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Acknowledgements

The author thanks the referee for useful remarks.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics and Informatics Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Antanas Laurinčikas

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  1. Antanas Laurinčikas
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Correspondence to Antanas Laurinčikas.

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The research is funded by the European Social Fund (Project No. 09.3.3-LMT-K-712-01-0037) under grant agreement with the Research Council of Lithuania (LMT LT).

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Laurinčikas, A. Approximation of analytic functions by an absolutely convergent Dirichlet series. Arch. Math. 117, 53–63 (2021). https://doi.org/10.1007/s00013-021-01616-x

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  • DOI: https://doi.org/10.1007/s00013-021-01616-x

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