Modular Forms
For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who has revised it substantially for the English edition. It sets out to provide the reader with the basic knowledge of elliptic m
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Toshitsune Miyake
Modular Forms With n Figures
~Springer
Toshitsune Miyake Hokkaido University Department of Mathematics o6o-o810 Sapporo, Japan e-mail: [email protected]
Translator Yoshitaka Maeda Hokkaido University Department of Mathematics o6o-o810 Sapporo, Japan e-mail: [email protected]
The first English edition was published as a monograph in 1989 by Springer-Verlag Berlin Heidelberg GmbH.
ISBN 978-3-662-22188-4 ISBN 978-3-540-29593-8 (eBook) DOI 10.1007/978-3-540-29593-8
Title of the original Japanese edition: "Hokei keishiki to seisiiron" © Kinokuniya Company Ltd., Tokyo, 1976.
Library of Congress Control Number: 2005936235
Mathematics Subject Classification (2ooo ): nFo3, nFo6, nFn, nF12, nF27, 11F3o, uF66, nGo5, nMo6, nR42, nR52, nR56 ISSN 1439-7382
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Softcover reprint of the hardcover 1st edition 2006 The use of general descriptive names, registered names, trademarks, 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.
Typesetting: Macmillan India Ltd., Bangalore Production: LE-TJiX jelonek, Schmidt & Vockler GbR, Leipzig Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
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Preface
Modular forms play an essential role in Number Theory. Furthermore the importance of modular forms has continued to grow in many areas of mathematics including the infinite dimensional representation theory of Lie groups and finite group theory. The aim of this book is to introduce some basic theory of modular forms of one variable. Originally this book was written in Japanese under the title "Automorphic forms and Number Theory" by Koji Doi and myself and published by Kinokuniya, Tokyo, in 1976. When the English translation was planned, the first named author proposed that only the chapters written mainly by me be translated together with some additional material and published under my sole authorship. In Chapters 1 and 2, the general theory of Fuchsian groups, automorphic forms and Heeke algebras is discussed. In Chapter 3, I summarize some basic results on Dirichlet series which are necessary in the succeeding chapters. In Chapter 4, the classical theories of modular groups and modular for
