Read Anywhere and on Any Device!

Subscribe to Read | $0.00

Join today and start reading your favorite books for Free!

Create Free Account

Topics in Nevanlinna Theory

0/5 ( ratings)

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 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.

Language: English

Pages: 180

Format: Paperback

Publisher: Springer

Release: July 24, 1990

ISBN: 3540527850

ISBN 13: 9783540527855

Topics in Nevanlinna Theory

0/5 ( ratings)

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 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.

Language: English

Pages: 180

Format: Paperback

Publisher: Springer

Release: July 24, 1990

ISBN: 3540527850

ISBN 13: 9783540527855

More books from Serge Lang

Linear Algebra

3.8/5 ( ratings)

A First Course in Calculus

4.3/5 ( ratings)

Calculus of Several Variables

4.1/5 ( ratings)

The Beauty of Doing Mathematics: Three Public Dialogues

4.1/5 ( ratings)

Real and Functional Analysis (Graduate Texts in Mathematics)

3.7/5 ( ratings)

Undergraduate Analysis

Math!: Encounters with High School Students

4.1/5 ( ratings)

Differential and Riemannian Manifolds

3.6/5 ( ratings)

Undergraduate Algebra

Basic Analysis Of Regularized Series And Products

Spherical Inversion on Sln(r)

Solutions Manual for Geometry: A High School Course

Abelian Varieties

Frobenius Distributions In Gl2 Extensions: Distribution Of Frobenius Automorphisms In Gl2 Extensions Of The Rational Numbers (Lecture Notes In Mathematics)

SL2 (R)

Introduction to Linear Algebra (Undergraduate Texts in Mathematics)

Basic Mathematics

The Heat Kernel and Theta Inversion on SL2(C) (Springer Monographs in Mathematics)

Real Analysis

Complex Analysis

Rate this book!

Write a review?