Skip to main content
SpringerLink
Log in

A Bohr–Jessen Type Theorems for the Epstein Zeta-Function: III

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In the paper, joint continuous and discrete limit theorems with explicitly given limit measures for a collection of Epstein’s zeta-functions are proved. The theorems generalize one-dimensional limit theorems obtained in Laurinčikas and Macaitienė (Results Math 73(4):148, 2018; Results Math 74:25, 2020).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bateman, P.T., Grosswald, E.: On Epstein’s zeta function. Acta Arith. 9, 365–373 (1964)

    Article  MathSciNet  Google Scholar 

  2. Billingsley, P.: Convergence of Probability Measures, p. 253. Willey, New York (1968)

    MATH  Google Scholar 

  3. Cramér, H., Leadbetter, M.R.: Stationary and Related Processes. Wiley, New York (1967)

    MATH  Google Scholar 

  4. Dubickas, A., Laurinčikas, A.: Joint discrete universality of Dirichlet L-functions. Arch. Math. 104(1), 25–35 (2015)

    Article  MathSciNet  Google Scholar 

  5. Epstein, P.: Zur Theorie allgemeiner Zetafunktionen. Math. Ann. 56, 615–644 (1903)

    Article  MathSciNet  Google Scholar 

  6. Fomenko, O.M.: Order of the Epstein zeta-function in the critical strip. J. Math. Sci. 110(6), 3150–3163 (2002)

    Article  MathSciNet  Google Scholar 

  7. Hecke, E.: Über Modulfunktionen und die Dirichletchen Reihen mit Eulerscher Produktentwicklung. I, II. Math. Ann. 114(1–28), 316–351 (1937)

    Article  MathSciNet  Google Scholar 

  8. Iwaniec, H.: Topics in Classical Automorphic Forms, Graduate Studies in Mathematics, vol. 17. American Mathematical Society, Providence (1997)

    MATH  Google Scholar 

  9. Korsakienė, D., Laurinčikas, A., Šiaučiūnas, D.: Joint discrete universality of Dirichlet \(L\)-functions. II. Chebysh. Sb. 16(1), 205–218 (2015)

    MathSciNet  MATH  Google Scholar 

  10. Laurinčikas, A., Macaitienė, R.: A Bohr–Jessen type theorem for the Epstein zeta-function. Results Math. 73(4), 148 (2018)

    Article  MathSciNet  Google Scholar 

  11. Laurinčikas, A., Macaitienė, R.: A Bohr–Jessen type theorem for the Epstein zeta-function. II. Results Math. 74, 25 (2020)

    Article  MathSciNet  Google Scholar 

  12. Nakamura, T., Pańkowski, Ł.: On zeros and \(c\)-values of Epstein zeta-functions. Šiauliai Math. Semin. 8(16), 181–195 (2013)

    MathSciNet  MATH  Google Scholar 

  13. Selberg, A., Chowla, S.: On Epstein’s Zeta function. J. Reine Angew. Math. 227, 86–110 (1967)

    MathSciNet  MATH  Google Scholar 

  14. Shiryaev, A.N.: Probability, Graduate Texts in Mathematics, vol. 95, 2nd edn, p. 636. Springer, Berlin (1996)

    Google Scholar 

  15. Taylor, P.R.: The functional equation for Epstein’s zeta-function. Q. J. Math. 11, 177–182 (1940)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Antanas Laurinčikas

  2. Institute of Regional Development, Šiauliai Academy, Vilnius University, Šiauliai, Lithuania

    Renata Macaitienė

  3. Faculty of Business and Technologies, Šiauliai State College, Šiauliai, Lithuania

    Renata Macaitienė

Authors
  1. Antanas Laurinčikas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renata Macaitienė
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renata Macaitienė.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Laurinčikas, A., Macaitienė, R. A Bohr–Jessen Type Theorems for the Epstein Zeta-Function: III. Results Math 76, 105 (2021). https://doi.org/10.1007/s00025-021-01422-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-021-01422-5

Keywords

Mathematics Subject Classification

Search

Navigation