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Topics in Nevanlinna Theory

  • Book
  • © 1990

Overview

Editors:
  1. Serge Lang
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  2. William Cherry
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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1433)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-2
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  2. Nevanlinna theory in one variable

    • Serge Lang
    Pages 9-55

  3. Equidimensional higher dimensional theory

    • Serge Lang
    Pages 57-107

  4. Nevanlinna Theory for Meromorphic Functions on Coverings of C

    • William Cherry
    Pages 113-142

  5. Equidimensional Nevanlinna Theory on Coverings of Cn

    • William Cherry
    Pages 143-168

  6. Back Matter

    Pages 169-174
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Topics in Nevanlinna Theory

  • Editors: Serge Lang, William Cherry

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093846

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52785-5Published: 24 July 1990

  • eBook ISBN: 978-3-540-47146-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: CLXXXIV, 180

  • Topics: Analysis, Differential Geometry, Algebraic Geometry, Number Theory

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