Skip to main content
SpringerLink
Log in

Derivatives of Meromorphic Functions of Finite Order

  • Published:
Computational Methods and Function Theory Aims and scope Submit manuscript

Abstract

A result is proved concerning meromorphic functions \(f\) of finite order in the plane such that all but finitely many zeros of \(f''\) are zeros of \(f'\).

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. Barry, P.D.: On a theorem of Kjellberg. Quart. J. Math. Oxf. 15(2), 179–191 (1964)

    Google Scholar 

  2. Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoam. 11, 355–373 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gundersen, G.: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J. Lond. Math. Soc. 37(2), 88–104 (1988)

    Google Scholar 

  4. Hayman, W.K.: Meromorphic Functions. Clarendon Press, Oxford (1964)

  5. Hayman, W.K.: The local growth of power series: a survey of the Wiman-Valiron method. Canad. Math. Bull. 17, 317–358 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hayman, W.K.: Subharmonic Functions, vol. 2. Academic Press, London (1989)

    MATH  Google Scholar 

  7. Hinchliffe, J.D.: The Bergweiler–Eremenko theorem for finite lower order. Results Math. 43, 121–128 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Langley, J.K.: The second derivative of a meromorphic function of finite order. Bull. Lond. Math. Soc. 35, 97–108 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Langley, J.K.: Logarithmic singularities and the zeros of the second derivative. Comput. Methods Funct. Theory 9(2), 565–578 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lewis, J., Rossi, J., Weitsman, A.: On the growth of subharmonic functions along paths. Ark. Mat. 22, 104–114 (1983)

    MathSciNet  Google Scholar 

  11. Nevanlinna, R.: Eindeutige Analytische Funktionen, 2nd edn. Springer, Berlin (1953)

    Book  MATH  Google Scholar 

  12. Pommerenke, C.: Boundary behaviour of conformal maps. In: Grundlehren der Mathematischen Wissenschaften, vol. 299. Springer, Berlin (1992)

  13. Tsuji, M.: Potential Theory in Modern Function Theory. Maruzen, Tokyo (1959)

    MATH  Google Scholar 

  14. Yamanoi, K.: Zeros of higher derivatives of meromorphic functions in the complex plane. Proc. Lond. Math. Soc. 106(4), 703–780 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author thanks the referee for a very careful reading of the paper and for some helpful suggestions to improve its readability.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham,  NG7 2RD, UK

    J. K. Langley

Authors
  1. J. K. Langley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. K. Langley.

Additional information

Communicated by Lawrence Zalcman.

Dedicated to the memory of Fred Gehring.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Langley, J.K. Derivatives of Meromorphic Functions of Finite Order. Comput. Methods Funct. Theory 14, 195–207 (2014). https://doi.org/10.1007/s40315-013-0039-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40315-013-0039-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation