Lecture Notes in Mathematics

Topics in Nevanlinna Theory

Authors: Lang, Serge, Cherry, William

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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.

Table of contents (4 chapters)

  • Nevanlinna theory in one variable

    Lang, Serge

    Pages 9-55

  • Equidimensional higher dimensional theory

    Lang, Serge

    Pages 57-107

  • Nevanlinna Theory for Meromorphic Functions on Coverings of C

    Cherry, William

    Pages 113-142

  • Equidimensional Nevanlinna Theory on Coverings of Cn

    Cherry, William

    Pages 143-168

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-47146-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-52785-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Nevanlinna Theory
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1433
Copyright
1990
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-47146-2
DOI
10.1007/BFb0093846
Softcover ISBN
978-3-540-52785-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
CLXXXIV, 180
Topics