On the Class Number of Abelian Number Fields Extended with Tables by
With this translation, the classic monograph Über die Klassenzahl abelscher Zahlkörper by Helmut Hasse is now available in English for the first time. The book addresses three main topics: class number formulas for abelian number fields; expressions of th
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On the Class Number of Abelian Number Fields Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
On the Class Number of Abelian Number Fields
Helmut Hasse
On the Class Number of Abelian Number Fields Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
123
Helmut Hasse Hamburg, Germany Translated by Mikihito Hirabayashi Kanazawa Institute of Technology Ishikawa, Japan
The book is a translation of the German edition - two chapters are added as reprints. ISBN 978-3-030-01510-7 ISBN 978-3-030-01512-1 (eBook) https://doi.org/10.1007/978-3-030-01512-1 Library of Congress Control Number: 2018961405 Mathematics Subject Classification (2010): 11-XX, 11Rxx, 11R37, 11R29, 12-XX Part II Chapter 4 reprinted with kind permission of Kanazawa Medical University from: Ken-ichi Yoshino and Mikihito Hirabayashi, On the Relative Class Number of the Imaginary Abelian Number Field I, Memoirs of the College of Liberal Arts, Vol. 9, December, p. 5–53, © Kanazawa Medical University 1981. Part II Chapter 5 reprinted with kind permission of Kanazawa Medical University from: Ken-ichi Yoshino and Mikihito Hirabayashi, On the Relative Class Number of the Imaginary Abelian Number Field II, Memoirs of the College of Liberal Arts, Vol. 10, December, p. 33–81, © Kanazawa Medical University 1982. Corrected printing 2015 English translation of the German reprint published by Springer-Verlag Berlin, Heidelberg, 1985 © Springer Nature Switzerland AG 1952, 1985, 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
Jacques Martinet has sketched the development of the main ideas in the theory of cyclotomic fields from the publication of Hasse’s monograph up to the heydays of Iwasawa theo
