Log in

On the functional equation of certain Dirichlet series

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

References

  1. Doi, K., Naganuma, H.: On the algebraic curves uniformized by arithmetical automorphic functions. Ann. of Math.86, 449–460 (1967).

    Google Scholar 

  2. Eichler, M.: Über die Darstellbarkeit von Modulformen durch Thetareihen. J. Reine Angew. Math.195, 156–171 (1955).

    Google Scholar 

  3. —: Zur Zahlentheorie der Quaternion Algebra.Ibid. 127–151.

    Google Scholar 

  4. Erdelyi, A.: Higher transcendental functions, vol. 2. New York: McGraw-Hill 1953.

    Google Scholar 

  5. Hecke, E.: Mathematische Werke. Göttingen: Vandenhoeck & Ruprecht 1959.

    Google Scholar 

  6. Maass, H.: Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann.121, 141–183 (1949).

    Google Scholar 

  7. Rankin, R.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions II. Proc. Camb. Phil. Soc.35, 357–372 (1939).

    Google Scholar 

  8. Shimizu, H.: On zeta functions of quaternion algebras. Ann. of Math.81, 166–193 (1965).

    Google Scholar 

  9. Shimura, G.: On Dirichlet series and abelian varieties attached to automorphic forms. Ann. of Math.76, 237–294 (1962).

    Google Scholar 

  10. Siegel, C. L.: Lectures on advanced analytic number theory. Tata Institute of Fundamental Research, Bombay 1961.

    Google Scholar 

  11. Weil, A.: Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann.168, 149–156 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported in part by National Science Foundation grant NSF GP-7952X.

Research supported in part by Army Research Office—Durham grant ARO-D-31-124-G892.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Doi, K., Naganuma, H. On the functional equation of certain Dirichlet series. Invent Math 9, 1–14 (1969). https://doi.org/10.1007/BF01389886

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389886

Keywords

Navigation