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Friedrich Hirzebruch · Thomas Berger  Rainer Jung

Manifolds and modular forms

Friedrich Hirzebruch Thomas ßerger Rainer Jung

Manifolds and Modular Forms

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Edited by Klos Diederich Vol. E 1:

G. Hector/U. Hirsch: Introduction to the Geometry of Foliations, Part A

Vol. E2:

M. Knebuschl M. Koister: Wittrings

Vol. E3:

G. Hectorl U. Hirsch: Introduction to the Geometry of Foliations, Part B

Vol. E4:

M. Laska: Elliptic Curves of Number Fields with Prescribed Reduction Type lout of printl

Vol. E5:

P. Stiller: Automorphic Forms and the Picard Number of an Elliptic Surface

Vol. E6:

G. Faltings/G. Wüstholz et al.: Rational Points*

Vol. E7:

W. StoII: Value Distribution Theory for Meromorphic Maps

Vol. E8:

W. von Wahl: The Equations of Navier-Stokes and Abstract Parabolic Equations lout of printl

Vol. E9:

A. Howardl P.-M. Wong (Eds.l: Contributions to Severol Complex Variables

Vol. E 10: A. J. Tromba (Ed.l: Seminar of New Results in Nonlinear Partial Differential Equations* Vol. E 11:

M. Yoshida: Fuchsian Differential Equations*

Vol. E 12:

R. Kulkarni, U. Pinkall (Eds.l: Conformal Geometry*

Vol. E 13: Y. Andre: G-Functions and Geometry* Vol. E 14:

U. Cegrell: Capacities in Complex Analysis

Vol. E 15: J -Po Serre: Lectures on the Mordell-Weil Theorem Vol. E 16:

K.lwasaki/H. KimurolS. Shimomuro/M. Yoshida: From Gauss to Painleve

Vol. E 17:

K. Diederich (Ed.l: Complex Analysis

Vol. E 18: W W.

J. Hulsbergen: Conjectures in Arithmetic Aigebraic Geometry

Vol. E 19:

R. Racke: Lectures on Nonlinear Evolution Equations

Vol. E20:

F. Hirzebruch, Th. Berger, R. Jung: Manifolds and Modular Forms*

*A Publicatian of the Max-Planck-Institut für Mathematik, Bonn

Volumes of the German-Ianguage subseries 'Äspekte der Mathematik" are listed at the end of the book.

Friedrich Hirzebruch Thomas ßerger Rainer Jung

Manifolds and Modular Forms Translated by Peter S. Landweber A Publication of the Max-Planck-Institut für Mathematik, Bonn

aI vleweg

Professor Dr. Friedrich Hirzebruch, Thomas Berger, and Rainer Jung Max-Planck-Institut für Mathematik Gottfried-Claren-Str.26 5300 Bonn 3 Germany

ISBN 978-3-528-06414-3

ISBN 978-3-663-14045-0 (eBook)

DOI 10.1007/978-3-663-14045-0

Appendix III: El/iptic genera 01 level N lor complex manijolds reprinted with perrnission of Kluwer Academic Publishers Mathematical Subject Classification: 57-02, llFll, 33C45, 33E05, 55N22, 55RlO, 57R20, 58GlO All rights reserved © Springer Fachmedien Wiesbaden, 1992 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, BraunschweiglWiesbaden in 1992.

No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanicaJ, photocopying or otherwise, without prior permission of the copyright holder.

Cover design: Wolfgang Nieger, Wiesbaden Printed on acid-free paper

Preface During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". Iwanted to develop the theory of "Elliptic Genera" and to leam it mysel

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