Introduction to the Theory of Algebraic Numbers and Fuctions
Published on 1. January 1966
323 pages
978-0-08-087335-0 (ISBN)
Description
Introduction to the Theory of Algebraic Numbers and Fuctions
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Content
- Front Cover
- Introduction to The Theory of Algebraic Numbers and Functions
- Copyright Page
- Contents
- Preface to The English Edition
- Preface to The German Edition
- Introduction
- 1. The Subject
- 2. The Method
- Table of Several Abbreviations and Symbols
- Chapter I. Linear Algebra
- 1. Modules in Principal Ideal Domains
- 2. Systems of Linear Inequalities
- 3. Linear Divisors
- 4. Traces, Norms, and Discriminants
- Appendix to Chapter I: The Theta Function
- 1. The Symplectic Group
- 2. Theta Functions for Quadratic Forms
- Chapter II. Ideals and Divisors
- 1. Ideals
- 2. Local Rings
- 3. Ideals in Different Fields
- the Norm
- 4. The Complement, Different, and Discriminant
- 5. Divisors
- 6. Decomposition of Prime Ideals in Galois Extensions
- Appendix to Chapter II: Topics from the Theory of Algebraic Number Fields
- 1. The Finiteness Theorems
- 2. Quadratic Number Fields and Cyclotomic Fields
- Chapter III. Algebraic Functions and Differentials
- 1. Power Series Expansions of Algebraic Functions
- 2. Algebraic Function Fields
- 3. The Riemann-Roch Theorem
- 4. Differentials
- 5. Differentials and Principal Part Systems
- 6. Reduction of a Function Field with Respect to a Prime Ideal of the Constant Field
- Chapter IV. Algebraic Functions over the Complex Number Field
- 1. Riemann Surfaces
- 2. Fields of Elliptic Functions
- 3. The Group of Divisor Classes of Degree 0
- 4. Modular Functions
- Chapter V. Correspondences between Fields of Algebraic Functions
- 1. The Correspondences
- 2. Representations of Correspondences in the Space of Differentials
- 3. Modular Functions
- 4. Castelnuovo's Inequality
- 5. Applications in Number Theory
- 6. Elliptic Function Fields
- Author Index
- Subject Index
