Topics in Nevanlinna Theory (Lecture Notes in Mathematics)

Serge Lang

ISBN 10: 3540527850 / ISBN 13: 9783540527855

Editore: Springer Berlin Heidelberg, 1990

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Type: Book Plain label inside cover.Pages a little darkened. Codice articolo 052387

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Titolo: Topics in Nevanlinna Theory (Lecture Notes ...

Casa editrice: Springer Berlin Heidelberg

Data di pubblicazione: 1990

Legatura: Paperback

Condizione: Good

Condizione sovraccoperta: No d/j as Published

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Riassunto:

These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp. Cn. Conjecturally best possible error terms are obtained following a method of Ahlfors and Wong. This is especially significant when obtaining uniformity for the error term w.r.t. coverings, since the analytic yields case a strong version of Vojta's conjectures in the number-theoretic case involving the theory of heights. The counting function for the ramified locus in the analytic case is the analogue of the normalized logarithmetic discriminant in the number-theoretic case, and is seen to occur with the expected coefficient 1. The error terms are given involving an approximating function (type function) similar to the probabilistic type function of Khitchine in number theory. The leisurely exposition allows readers with no background in Nevanlinna Theory to approach some of the basic remaining problems around the error term. It may be used as a continuation of a graduate course in complex analysis, also leading into complex differential geometry.

Contenuti:

Nevanlinna theory in one variable.- Equidimensional higher dimensional theory.- Nevanlinna Theory for Meromorphic Functions on Coverings of C.- Equidimensional Nevanlinna Theory on Coverings of Cn.