Skip to main content
SpringerLink
Log in

Growth properties of vector valued Dirichlet series with complex exponents

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

Several authors have studied the growth properties of Dirichlet series and vector valued Dirichlet series (VVDS). Wen Ping Huang, Ju Hong Ning and Jin Tu have obtained various results by considering Dirichlet series with complex exponents. In this paper we obtainthe characterizations of order and type of vector valued Dirichlet series which generalize some well known results for growth of classical Dirichlet series. Further we have tried to study the growth properties of holomorphic vector valued Dirichlet series with complex exponents.

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. Akanksha, Srivastava, G.S.: Spaces of vector valued Dirichletseries in a half plane. Front. Math. China 9, 1239–1252 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Boivin, A., Zhu, C.Z.: The growth of an entire function and its Dirichlet coefficients and exponents. J. Complex Var. Theory Appl 48(5), 397–415 (2003)

    MathSciNet  MATH  Google Scholar 

  3. Huang, W.P., Ning, J.H., Tu, J.: Order and type of the generalized Dirichlet series. J. Math. Res. Expo. 29(6), 1041–1046 (2009)

    MathSciNet  Google Scholar 

  4. Juneja, O.P., Nandan, K.: On the growth of analytic functions represented by Dirichlet series. Portugal. Math. 37, 125–133 (1978)

    MathSciNet  MATH  Google Scholar 

  5. Khoi, L.H.: Holomorphic Dirichlet series in the half plane. Vietnam J. Math. 26, 259–271 (1998)

    MathSciNet  MATH  Google Scholar 

  6. Nandan, K: On the maximum term and maximum modulus of analytic functions represented by Dirichlet series. Ann. Polon. Math. XXVIII, 213–222 (1975)

  7. Ritt, J.F.: On certain points in the theory of Dirichlet series. Am. J. Math 50, 73–83 (1928)

    Article  MathSciNet  MATH  Google Scholar 

  8. Srivastava, B.L.: A study of spaces of certain classes of vector valued Dirichlet series, thesis, I.I.T Kanpur (1983)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector-62, Noida, 201307, India

    Akanksha & G. S. Srivastava

Authors
  1. Akanksha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. S. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. S. Srivastava.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akanksha, Srivastava, G.S. Growth properties of vector valued Dirichlet series with complex exponents. Afr. Mat. 29, 601–614 (2018). https://doi.org/10.1007/s13370-018-0563-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-018-0563-7

Keywords

Mathematics Subject Classification

Search

Navigation