Modular Functions of one Variable V Proceedings International Confer

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601 Modular Functions of one Variable V Proceedings International Conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik July 2-14, 1976

Edited by J.-P. Serre and D. B. Zagier

Springer-Verlag Berlin Heidelberg New York 1977

Editors Jean-Pierre Serre College de France 75231 Paris Cedex 05 France

Don Bernard Zagier Mathematisches lnstitut der Universitat Bonn Wegelerstr. 10 53 Bonn/BRD

Library of Congress. Cataloging in Publication Data

Main entry under title: Modular functions of one variable V- •

(Lecture notes in mathematics ; 601) 1. Functions, Modular-Congresses. 2. Algebraic number theory-Congresses. I. Serre, Jean-Pierre. II. Zagier, Don Bernard. III. Series: Lecture notes in mathematics (Berlin) ; 6ol) QA3.L2B no. 601, etc. cW43 1 510 1 .Bs 77-2214B c515 1 ·9J

AMS Subject Classifications {1970): 10C15, 10005, 10025, 12A99, 14H45, 14K22, 14K25 ISBN 3-540-08348-0 ISBN 0-387-08348-0

Springer-Verlag Berlin Heidelberg New York Springer-Verlag New York Heidelberg Berlin

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.

© by Springer-Verlag Berlin Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.

2141/3140-543210

P RE F ACE

In view of the increased interest and rapid developments in the theory of modular forms which followed the 1972 conference in Antwerp, it was decided to have a second meeting on the same subject. in the summer of 1976 in place of the annual

This meeting was held in Bonn ~athematische

Arbeitstagung.

The

organizers were F. Hirzebruch, J-P. Serre and D. Zagier. The proceedings of the conference are being published in two parts, as a continuation of the four volumes of proceedings of the Antwerp conference (Lecture Notes Nos. 320, 349, 350 and 476).

The present volume is mostly

algebraic (congruence properties of modular forms, modular curves and their rational points, etc.), whereas the second volume will be more analytic and also include some papers on modular forms in several variables. The conference was sponsored by the "Special Research Area in Theoretical ~thematics"

(Sonderforschungsbereich 40 der Deutschen Forschungsgemeinschaft)

at the University of Bonn, with further support from the College de France and the International Mathematical Union.

We would like to thank these organizations

as well as the National Science Foundation, whose generous financial support made it possible for a large number of mathematicians from the United States to attend the meeting.

We would also like to thank W. Kuyk of the University of

Antwerp, who placed secretarial help at our disposal for th