Overview

This book gives an exposition of the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. The following topics are treated: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. Each chapter ends with exercises and a short review of the relevant literature up to 2003. The bibliography has over 3400 items.

Full Product Details

Author:   Wladyslaw Narkiewicz
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   3rd ed. 2004
Dimensions:   Width: 15.20cm , Height: 3.90cm , Length: 22.90cm
Weight:   2.620kg
ISBN:  

9783540219026

ISBN 10:   3540219021
Pages:   712
Publication Date:   24 June 2004
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Dedekind Domains and Valuations.- 2. Algebraic Numbers and Integers.- 3. Units and Ideal Classes.- 4. Extensions.- 5. P-adic Fields.- 6. Applications of the Theory of P-adic Fields.- 7. Analytical Methods.- 8. Abelian Fields.- 9. Factorizations 9.1. 485Elementary Approach.- Appendix I. Locally Compact Abelian Groups.- Appendix II. Function Theory.- Appendix III. Baker’s Method.- Problems.- References.- Author Index.- List of Symbols.

Reviews

Aus den Rezensionen zur 3. Auflage: Das vorliegende Buch ist die dritte Auflage des Standardwerks uber analytische Aspekte der algebraischen Zahlentheorie. ! das Buch ist durchgehend in LaTeX gesetzt, was die Lekture angenehmer gestaltet. ! Durch die Aktualisierung wird dieses Buch sicher fur die nachsten Jahre ein wichtiges Referenzwerk in diesem Gebiet bleiben. (P. Grabner, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 41 f.)

From the reviews of the third edition: <p> This giant tome is a ~elementarya (TM) only in the sense of a ~classicala (TM) (for the first four chapters), and a ~analytica (TM) thereafter a ] . The main text of nine chapters has about 400 pages. There are extensive notes at the end of each chapter, covering a further 90 pages and giving additional background with references to the research literature. a ] is likely to be, for many years, a valuable resource for those already involved in serious research on algebraic number theory a ] . (John Baylis, The Mathematical Gazette, Vol. 89 (515), 2005) <p> The book gives an exposition of the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. a ] Each chapter ends with exercises and a short review of the relevant literature up to 2003. The bibliography has over 3400 items. (Zentralblatt fA1/4r Didaktik der Mathematik, November, 2004) <p> This is the third edition of a well-known textbook on algebraic number theory. a ] the author has thoroughly updated the comments at the end of each chapter and extended the bibliography accordingly. a ] for most professional number theorists one of this booka (TM)s most appealing features will be the carefully researched notes and the large number of references. These make it a real treasure house and ensure that this volume will be an indispensable work of reference for anyone working in or using algebraic number theory. (Ch. Baxa, Monatshefte fA1/4r Mathematik, Vol. 149 (2), 2006) <p> Narkiewicza (TM) tome, weighing in at xi + 708 pages, is an imposing work, ambitious in scope and even encyclopaedic a ] . Elementary and Analytic Theory ofAlgebraic Numbers is also well-written and eminently readable by a good and diligent graduate student. It would serve beautifully for a graduate-level course in number theory sans class-field theory. a ] Narkiewicza (TM) presentation is so clear and detailed that coverage of certain topics a ] is extremely beneficial. (Michael Berg, MathDL, September, 2005)

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