Advanced Topics in Computional Number Theory

Henri Cohen

578 pages, parution le 01/06/1999

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Résumé

The present book addresses a number of specific topics in computational number theory whereby the author is not attempting to be exhaustive in the choice of subjects. The book is organized as follows. Chapters 1 and 2 contain the theory and algorithms concerning Dedekind domains and relative extensions of number fields, and in particular the generalization to the relative case of the round 2 and related algorithms. Chapters 3, 4, and 5 contain the theory and complete algorithms concerning class field theory over number fields. The highlights are the algorithms for computing the structure of (Z_K/m)^*, of ray class groups, and relative equations for Abelian extensions of number fields using Kummer theory. Chapters 1 to 5 form a homogeneous subject matter which can be used for a 6 months to 1 year graduate course in computational number theory. The subsequent chapters deal with more miscellaneous subjects. Written by an authority with great practical and teaching experience in the field, this book together with the author's earlier book will become the standard and indispensable reference on the subject.

Contents

Preface

1: Fundamental Results and Algorithms in Dedekind Domains
2: Basic Relative Number Field Algorithms
3: The Fundamental Theorems of Global Class Field Theory
4: Computational Class Field Theory
5: Computing Defining Polynomials Using Kummer Theory
6: Computing Defining Polynomials Using Analytic Methods
7: Variations on Class and Unit Groups
8: Cubic Number Fields
9: Number Field Table Constructions

App. A: Theoretical Results
App. B: Electronic Information
App. C: Tables 533 Bibliography

Index of Notation 556
Index of Algorithms
General Index

L'auteur - Henri Cohen

Dr. Henri Cohen is Professor of Mathematics at the University of Bordeaux, France. His research interests are number theory in general, and computational number theory in particular.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Henri Cohen
Parution	01/06/1999
Nb. de pages	578
Format	16 x 24
Couverture	Relié
Poids	960g
Intérieur	Noir et Blanc
EAN13	9780387987279
ISBN13	978-0-387-98727-9