Nevanlinna's Theory of Value Distribution

The Second Main Theorem and its Error Terms
1. Auflage. Softcover version of original hardcover Auflage 2001
ISBN: 978-3-642-08568-0
Verlag: Springer

Buch, Englisch, 203 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 341 g

Reihe: Springer Monographs in Mathematics

On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis. On the other hand, the monograph also serves as a valuable reference for the research specialist because the authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its "number-theoretic digressions". These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

Zielgruppe

Research

Autoren/Hrsg.

Ye, Zhuan

Cherry, William

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

1. The First Main Theorem.- 2. The Second Main Theorem via Negative Curvature.- 3. Logarithmic Derivatives.- 4. The Second Main Theorem via Logarithmic Derivatives.- 5. Some Applications.- 6. A Further Digression into Number Theory: Theorems of Roth and Khinchin.- 7. More on the Error Term.- Glossary of Notation.