Introduction to Modular Forms
From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs
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Editors
M. Artin s. S. Chern 1. Coates 1. M. Frohlich H. Hironaka E Hirzebruch L. Honnander C. C. Moore 1. K. Moser M Nagata W Schmidt D. S. Scott Ya. G. Sinai 1. Tits M. Waldschmidt S. Watanabe Managing Editors
M. Berger B. Eckmann S. R S. Varadhan
Serge Lang
Introduction to Modular Forms With 9 Figures
Springer
Serge Lang Department of Mathematics Yale University 10 Hillhouse Avenue New Haven, CT 06520-8283, USA
Second Corrected Printing 1995
The AMS (MOS) classification scheme was made up before the subject of modular forms exploded. New numbers should be created for this subject. It is impossible at present to find numbers fitting this book appropriately. January 1995
S. Lang
ISBN 978-3-642-05716-8 ISBN 978-3-642-51447-0 (eBook) DOI 10.1007/978-3-642-51447-0 Library of Congress Cataloging-in-Publication Data Lang, Serge, 1927-. Introduction to modular forms/Serge Lang. p. (Grundlehren der mathematischen Wissenschaften; 222) "Second corrected printing" - T. p. verso. Includes bibliographical references (p. - ) and index. I. Forms, Modular. I. Title. II. Series. QA243.L257 1976b 512'.73-dc20 94-48556
cm. -
CIP
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 SpringerVerlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1976 Softcover reprint of the hardcover 15t edition 1976 Typesetting: William Clowes & Sons Limited, London, Beccles and Colchester 4113143-54321 0 Printed on acid-free paper SPIN 10476716
Foreword
This book is intended as a partial survey for the elementary parts of an exceptionally active field which found a resurgence of interest over the last 8 years, after being almost forgotten for 30 years. I have attempted to put together some of the basic facts to make it easier for those who don't know the subject, to get some idea where it is going in the arithmetic direction, and how to get into it. I hope that the reader will find this book a helpful introduction to the Antwerp Conference volumes (Springer Lecture Notes). It is unfortunate that Hecke's Institute Lecture Notes [H] never received wide distribution nor attention, and that they were omitted from his collected works. They summarize a great deal of his insights into modular forms. Ogg's book [0], for instance, follows almost the same table of contents, the main additions being the Petersson scalar product and Weil's theorem on functional equations, which Hecke did not have. Considering the progress which has been made since then, they have perhaps mostly historical interest, but I feel that even now, it is profitable
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