Topics in Nevanlinna Theory: 1433 (Lecture Notes in Mathematics, 1433) - Softcover

Lang, Serge; Cherry, William

Softcover

ISBN 10: 3540527850 ISBN 13: 9783540527855

Publisher: Springer, 1990

Synopsis

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.

About this title

Synopsis

Intended for those with no background in Nevanlinna theory, this book aims to enable the reader to approach some of the basic problems around the error term, covering complex analysis and complex differential geometry.

Edition details

• Publisher: Springer
• Publication date: 1990
• Language: English
• ISBN 10: 3540527850
• ISBN 13: 9783540527855
• Binding: Paperback
• Number of pages: 364