Hostname: page-component-788cddb947-t9bwh Total loading time: 0 Render date: 2024-10-15T02:40:06.119Z Has data issue: false hasContentIssue false

The lemma of the logarithmic derivative for subharmonic functions

Published online by Cambridge University Press:  24 October 2008

Walter Rudin
Affiliation:
University of Wisconsin, Madison, WI 53706, U.S.A.

Extract

The classical statement of the lemma in question [7], [3] is about meromorphic functions f on ℂ and says that

for all r > 0, with the possible exception of a set of finite Lebesgue measure. Here T(r, f) is the Nevanlinna characteristic of f. The lemma plays an important role in value distribution theory.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Patrick, Ahern and Walter, Rudin. Periodic automorphisms of ℂn. Indiana U. Math. J. 44 (1995), 287303.Google Scholar
[2]Walter, Hayman. On the characteristic of functions meromorphic in the plane and of their integrals. Proc. London Math. Soc. 14A (1965), 93128.Google Scholar
[3]Walter, Hayman. Meromorphic functions (Oxford University Press, 1964).Google Scholar
[4]Hayman, W. K. and Kennedy, P. B.. Subharmonic functions (Academic Press, 1976).Google Scholar
[5]Aimo, Hinkkanen. A sharp form of Nevanlinna's second fundamental theorem. Inv. Math. 108 (1992), 549574.Google Scholar
[6]Joseph, Miles. A sharp form of the lemma on the logarithmic derivative. J. London Math. Soc. 45 (1992), 243260.Google Scholar
[7]Rolf, Nevanlinna. Eindeutige analylische Funktionen, 2nd ed. (Springer-Verlag, 1953).Google Scholar
[8]Ryll, J. and Wojtaszczyk, P.. On homogeneous polynomials on a complex ball. Trans. Amer. Math. Soc. 276 (1983), 107116.CrossRefGoogle Scholar
[9]Walter, Rudin, New constructions of functions holomorphic in the unit bali ofn. CBMS Regional Conference Series in Mathematics, No. 63, 1986.CrossRefGoogle Scholar
[10]Vitter, A., The lemma of the logrithmic derivative in several complex variables. Duke Math. J. 44 (1977), 89104.CrossRefGoogle Scholar
[11]Zhuan, Ye.On Nevanlinna's error terms. Duke Math. J. 64 (1991), 243260.Google Scholar