Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics, 193)

Cohen, Henri

ISBN 10: 0387987274 / ISBN 13: 9780387987279

Edité par Springer, 1999

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N° de réf. du vendeur 9780387987279

Détails bibliographiques

• Titre: Advanced Topics in Computational Number Theory (Graduate Texts in Mathematics, 193)
• Éditeur: Springer
• Date de parution: 1999
• Langue: anglais
• ISBN à 10 chiffres: 0387987274
• ISBN à 13 chiffres: 9780387987279
• Reliure: Couverture rigide
• État de l'article: Good

A propos de ce titre

Synopsis

Preliminary Text. Do not use. 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. 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.

Présentation de l'éditeur

This book addresses a number of specific topics in computational number theory centered on class field theory and relative extensions of number fields. Most of the material is new from the algorithmic standpoint. 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, 5, and 6 contain the theory and complete algorithms concerning class field theory over number fields. The highlights are the algorithms for computing the structure of (zk/m)*, of ray class groups, and relative equations for Abelian extensions based on complex multiplication or Stark's conjectures. Together with Chapter 10, which contains complete proofs of several results used in the rest of the book that cannot easily be found in the existing literature, Chapters 1 to 6 form a homogeneous subject matter, which can be used for a 6-month to 1-year graduate course in computational number theory. The other 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, A Course in Computational Algebraic Number Theory (GTM 138), will become the standard and indispensable reference on the subject.