Algebraic Number Theory
"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algeb
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Editors
S. S. Chern B. Eckmann P. de la Harpe H. Hironaka F. Hirzebruch N. Hitchin 1. Hormander M.-A. Knus A. Kupiainen }. Lannes G. Lebeau M. Ratner D. Serre Ya.G. Sinai N.}. A. Sloane }.Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger }. Coates S. R. S. Varadhan
322
Springer-Verlag Berlin Heidelberg GmbH
Jurgen Neukirch
Algebraic Number Theory Translated from the German by Norbert Schappacher With 16 Figures
Springer
Jiirgen Neukircht Translator:
Norbert Schappacher U.F.R. de Mathematique et d'Informatique Universite Louis Pasteur 7, rue Rene Descartes F-67084 Strasbourg, France e-mail: [email protected]
The original German edition was published in 1992 under the title
Algebraische Zahlentheorie ISBN 3-540-54273-6 Springer-Verlag Berlin Heidelberg New York
Library of Congress Cataloging-in-Publication Data
Neukirch, lurgen, 1937-. [Algebraische zahlentheorie. English] Algebraic number
theory 1 Jiirgen Neukirch; translated from the German by Norbert Schappacher. p. cm. - (Grundlehren der mathematischen Wissenschaften; 322 Includes bibliographical references and index. ISBN 978-3-642-08473-7 ISBN 978-3-662-03983-0 (eBook) DOI 10.1007/978-3-662-03983-0 1. Algebraic number theory. 1. Title II. Series. QA247.N51713 1999 512'.74-dc21 99-21030 CIP
Mathematics Subject Classification (1991): u-XX, 14-XX
ISSN 0072-7830 ISBN 978-3-642-08473-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfIlm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH.
Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg New York in 1999
Softcover reprint of the hardcover 1st edition 1999
Cover design: MetaDesign plus GmbH, Berlin Photocomposed from the translator's LATEX files after editing and reformatting by Raymond Seroul, Strasbourg SPIN: 10994771 41/3111- 543 2 Printed on acid-free paper
Foreword
It is a very sad moment for me to write this "Geleitwort" to the English translation of Jiirgen Neukirch's book on Algebraic Number Theory. It would have been so much better, if he could have done this himself.
But it is also very difficult for me to write this "Geleitwort": The book contains Neukirch's Preface to the German edition. There he himself speaks about his intentions, the content of the book and his personal view of the subject. What else can be said? It becomes clear from his Preface that Number Theory was Neukirch's favorite subject in mathematics. He was enthusiastic about it, and he was also able to implant this enthusiasm into the minds of his
