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Topics in Nevanlinna theory / Serge Lang, William Cherry

Main Author Lang, Serge, 1927-2005 Coauthor Cherry, William Country Alemanha. Publication Berlin : Springer-Verlag, cop. 1990 Description [2], 174 p. ; 25 cm Series Lecture notes in mathematics , 1433) ISBN 3-540-52785-0 CDU 517.53
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Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca Geral da Universidade do Minho
BGUMD 46637 Available 191432
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Enhanced descriptions from Syndetics:

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. 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.

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