Bernoulli Numbers and Zeta Functions
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. Th
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Tsuneo Arakawa Tomoyoshi Ibukiyama Masanobu Kaneko
Bernoulli Numbers and Zeta Functions
Springer Monographs in Mathematics
For further volumes: http://www.springer.com/series/3733
Tsuneo Arakawa • Tomoyoshi Ibukiyama Masanobu Kaneko
Bernoulli Numbers and Zeta Functions with an appendix by Don Zagier
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Tsuneo Arakawa (deceased 2003) Masanobu Kaneko Kyushu University Fukuoka, Japan
Tomoyoshi Ibukiyama (emeritus) Osaka University Osaka, Japan Don Zagier (Appendix) Max Planck Institute for Mathematics Bonn, Germany
ISSN 1439-7382 ISSN 2196-9922 (electronic) ISBN 978-4-431-54918-5 ISBN 978-4-431-54919-2 (eBook) DOI 10.1007/978-4-431-54919-2 Springer Tokyo Heidelberg New York Dordrecht London Library of Congress Control Number: 2014938983 Mathematics Subject Classification: 11B68, 11B73, 11M06, 11L03, 11M06, 11M32, 11M35 © Springer Japan 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Two subjects are treated in this book. The main subject is the theory of Bernoulli numbers, which are a series of rational numbers that appear in various contexts of mathematics, and the other subject is the related theory of zeta functions, which are very important in number theory. We hope that these are enjoyable subjects both for amateur mathematics lovers a
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