Skip to main content
Log in

Julia lines of entire functions of slow growth

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain sufficient conditions under which the Julia lines of entire functions of slow growth do not have finite exceptional values.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. A. Gol’dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  2. A. Ostrowski, “Über Folgen analytischer Funktionen und einige Verschärfungen des Picardschen Satzes,” Math. Z., 24, 215–258 (1926).

    Article  MathSciNet  Google Scholar 

  3. C. Constantinescu, “Einige Anwendungen des hyperbolischen Masses,” Math. Nachr., 15, 155–172 (1956).

    MATH  MathSciNet  Google Scholar 

  4. O. Lehto, “The spectral derivative of a meromorphic function in the neighborhood of an isolated singularity,” Comment. Math. Helv., 33, 196–205 (1959).

    MATH  MathSciNet  Google Scholar 

  5. O. Lehto and K. Virtanen, “On the behaviour of meromorphic functions in the neighborhood of an isolated singularity,” Ann. Acad. Sci. Fenn., 240, 15–26 (1957).

    Google Scholar 

  6. A. A. Gol’dberg, B. Ya. Levin, and I. V. Ostrovskii, “Entire and meromorphic functions,” in: VINITI Series in Contemporary Problems of Mathematics, Fundamental Trends [in Russian], Vol. 85, VINITI, Moscow (1991), pp. 5–186.

    Google Scholar 

  7. W. Hayman, “Slowly growing integral and subharmonic functions,” Comment. Math. Helv., 34, 75–84 (1960).

    MATH  MathSciNet  Google Scholar 

  8. S. Toppila, “Some remarks on exceptional values at Julia line,” Ann. Acad. Sci. Fenn. Ser. A, 456, 3–20 (1970).

    MathSciNet  Google Scholar 

  9. N. V. Zabolotskii and M. N. Sheremeta, “On slow growth of main characteristics of entire functions,” Mat. Zametki, 65, No. 2, 206–214 (1999).

    MATH  MathSciNet  Google Scholar 

  10. A. A. Gol’dberg and N. V. Zabolotskii, “Index of concentration of a subharmonic function of zero order,” Mat. Zametki, 24, No. 3, 34–46 (1983).

    MathSciNet  Google Scholar 

  11. A. V. Bratishchev and Yu. F. Korobeinik, “On some characteristics of growth of subharmonic functions,” Mat. Sb., 106, No. 1, 44–65 (1978).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 829–834, June, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zabolots’kyi, M.V. Julia lines of entire functions of slow growth. Ukr Math J 58, 937–944 (2006). https://doi.org/10.1007/s11253-006-0113-6

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0113-6

Keywords

Navigation