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Value distribution of certain monomials of algebroid functions

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Kari Katajamäki
Kari Katajamäki
Affiliation:
Department of Mathematics University of JoensuuP.O. Box 111 80101 Joensuu, Finland
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Abstract

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Hayman has shown that if f is a transcendental meromorphic function and n ≽ 3, then fn f′ assumes all finite values except possibly zero infinitely often. We extend his result in three directions by considering an algebroid function ω, its monomial ωn0 ω′n1, and by estimating the growth of the number of α-points of the monomial.

Keywords

Algebroid functionsdifferential polynomialsmonomials

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 398 - 404
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Clunie, J., ‘On a result of Hayman’, J. London Math. Soc. 42 (1967), 389–392.Google Scholar
[2]Hayman, W., ‘Picard values of meromorphic functions and their derivatives’, Ann. of Math. (2) 70 (1959), 9–42.CrossRefGoogle Scholar
[3]Hayman, W., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[4]Katajamäki, K., ‘Algebroid solutions of binomial and linear differential equations’, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes No. 90 (1993), 48pp.Google Scholar
[5]Katajamäki, K., ‘Value distribution of certain differential polynomials of algebroid functions’. Arch. Math. (Basel) 67 (1996), 422–429.CrossRefGoogle Scholar
[6]Mues, E., ‘Über ein Problem von Hayman’, Math. Z. 164 (1979), 239–259.Google Scholar
[7]Selberg, H., ‘Über die Wertverteilung der algebroiden Funktionen’, Math. Z. 31 (1930), 709–728.CrossRefGoogle Scholar
[8]Ullrich, E., ‘Über den Einfluß der Verzweigtheit einer Algebroide auf ihre Wertverteilung’, J. Reine Angew. Math. 167 (1932), 198–220.CrossRefGoogle Scholar
[9]Valiron, G., ‘Sur la dérivée des fonctions algébroïdes’, Bull. Soc. Math. France 59 (1931), 17–39.CrossRefGoogle Scholar