UID:
almahu_9947366693902882
Umfang:
1 online resource (341 p.)
ISBN:
1-281-76638-0
,
9786611766382
,
0-08-087335-9
Serie:
Pure and applied mathematics a series of monographs and textbooks ; 23
Originaltitel:
Einführung in die Theorie der algebraischen Zahlen und Funktionen.
Inhalt:
Introduction to the Theory of Algebraic Numbers and Fuctions
Anmerkung:
Description based upon print version of record.
,
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 FieldChapter 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
,
English
Weitere Ausg.:
ISBN 0-12-374570-5
Sprache:
Englisch
