Lang / Cherry Topics in Nevanlinna Theory

Erscheinungsjahr 2006
ISBN: 978-3-540-47146-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1433, 180 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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 Cresp. C n. 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.

Zielgruppe

Research

Autoren/Hrsg.

Lang, Serge

Cherry, William

Inhaltsverzeichnis

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.