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A Measure of Linear Independence for Some Exponential Functions II

Published online by Cambridge University Press:  20 November 2018

W. Dale Brownawell
W. Dale Brownawell*
Affiliation:
Penn State University, University Park, Pennsylvania
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This paper continues the investigations in [1] and [2] and extends the results of the latter paper to functions of several complex variables. Namely let λ : R>0 —> R>0 be monotonically increasing. (If λ is non-constant, we also require that log r = 0(λ(r)). We write / = 0(g) to mean that there is a constant C > 0 such that f(r) ≦ Cg(r) except possibly on a set of intervals of finite total length.) Let 0\ denote the set of meromorphic / on Cn for which the Nevanlinna characteristic function [5, p. 174] T(f, r) satisfies T(f, r) = 0(λ(r)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 341 - 346
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Brownawell, W. D., The algebraic independence of certain exponential functions, Can. J. Math. 28 (1976), 968–976.Google Scholar
2. Brownawell, W. D., A measure of linear independence for some exponential functions, in Baker, A. and Masser, D. W., eds, Transcendence Theory: Advances and Applications (Academic Press, London and New York, 1977).Google Scholar
3. Gauthier, P. M. and Hengartner, W., The value distribution of most functions of one or more complex variables, Annals of Math. 96 (1972), 31–52.Google Scholar
4. Griffiths, P. A., Entire Holomorphic Mappings in One and Several Complex Variables, (Princeton Univ. Press, Princeton, N.J., 1976).Google Scholar
5. Griffiths, P. A. and King, J., Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220.Google Scholar
6. Nevanlinna, R., Le Théorème de Picard-Borel et la Théorie des Fonctions Méromorphes, (Gauthier-Villars, Paris, 1929).Google Scholar
7. Vitter, A., The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), 89–104.Google Scholar