Skip to main content
SpringerLink
Log in

Analytic continuation of a class of dirichlet series

  • Published:
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We consider Dirichlet series of the type Σ(logk)n(k)(logk)ϑ-s. We prove the existence of an analytic continuation to the cut plane and give exact information about the singularity. We use this to generalize results, which occur in Ramanujan’s second notebook.

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. B. Berndt,Ramanujan’s Notebooks,Part II. Springer-Verlag, Berlin-New York (1989).

    MATH  Google Scholar 

  2. B. Berndt andR. Evans, Extensions of asymptotic expansions from chapter 15 of Ramanujans second note book.J. reine angew. Math. 361 (1985), 118–134.

    MATH  MathSciNet  Google Scholar 

  3. G. Doetsch,dbuch der Laplace-Transformation Birkhar-Verlag, Basel (1958).

    Google Scholar 

  4. P. Flajolet andA. M. Odlyzko, Singularity analysis of generating functions.SIAM J. Disc. Math. 3 (1990), 216–240.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Müller, On generalized Zeta-Functions at Negative Integers.Illinois J. Math. (2)32 (1988), 222–229.

    MATH  MathSciNet  Google Scholar 

  6. —, Über die meromorphe Fortsetzung einer Klasse verallgemeinerter Zeta-funktionen.Arch. Math. 58 (1992), 265–275.

    Article  MATH  Google Scholar 

  7. A. Selberg, Note on a paper by L. G. Sathe.J. Indian Math. Soc. B. 18 (1954), 83–87.

    MATH  MathSciNet  Google Scholar 

  8. J. M. ThuswaldnerAnalytische Methoden zur asymptotischen Untersuchung von Funktionalgleichungen und zur probabilistischen Analyse kombinatorischer Algorithmen. Thesis, Technische Universität Graz (1995)

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    P. J. Grabner & J. M. Thuswaldner

Authors
  1. P. J. Grabner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Thuswaldner
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors are supported by the Austrian National Bank project Nr. 4995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grabner, P.J., Thuswaldner, J.M. Analytic continuation of a class of dirichlet series. Abh.Math.Semin.Univ.Hambg. 66, 281–287 (1996). https://doi.org/10.1007/BF02940810

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02940810

Keywords

Search

Navigation