Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T00:43:41.438Z Has data issue: false hasContentIssue false

Asymptotic values of meromorphic functions of smooth growth

Published online by Cambridge University Press:  18 May 2009

J. M. Anderson
Affiliation:
Mathematics Department, University College, London WC1
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f denote a function, meromorphic in C. The question of when a deficient value of f, in the sense of Nevanlinna, is an asymptotic value has recently received some attention (see e.g. Hayman [6]). We assume acquaintance with the standard notation of the Nevanlinna theory ([[5] Chapter I) which we use without further mention. The following two theorems are known ([1] Theorem 4, and [6] Corollary 2).

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Anderson, J. M. and Clunie, J., Slowly growing meromorphic functions, Comment. Math Helv., 40 (1966), 267280.CrossRefGoogle Scholar
2.Essén, M., Slowly growing subharmonic functions II, to appear.Google Scholar
3.Goldberg, A. A. and Yeremenko, A. E., unpublished.Google Scholar
4.Hayman, W. K., Slowly growing integral and subharmonic functions, Comment. Math. Helv. 34 (1960), 7584.Google Scholar
5.Hayman, W. K., Meromorphic functions (Oxford, 1964).Google Scholar
6.Hayman, W. K., On Iversen's theorem for meromorphic functions with few poles, Acta Math. 141(1978) 115145.CrossRefGoogle Scholar
7.Nevanlinna, R., Analytic functions (Springer-Verlag, 1970).Google Scholar
8.Valiron, G., Sur les valeurs déficientes des fonctions méromorphes d'ordre nul. C.R. Acad. Sci. Paris 230 (1950), 4042.Google Scholar