John C. Polking, Series Editor
Peter Sarnak, Volume E ditor
Freydoon Shahidi, Volume EditorIAS/Park City Mathematics Institute runs math ematics education programs that bring
together high school mathematics teachers, researchers in mathematics and math ematics
education, undergraduate mathematics faculty, gr aduate students, and undergraduates to
participate in distinct but overlapping programs of research and education. This volume
conta ins the lecture notes from the Graduate Summer School progr a m.
2000 Mathematics Subject Classification. Primary 11 - 06, 11F12, 11F66, 11F70, 11F72,
11G40 , 11M36, 11T60, 22E46, 8 1Q50.Library of Congress Cataloging-in-Publication Data
Automorphic forms and applications / P eter Sarna k , F:reydoon Shahidi, editors.
p. cm. - (IAS/Park City mathematics series, IS SN 1079 -5634 ; v. 12)
Includes bibliographical r efer ences.
ISBN 978 -0- 8218 -2873-1 (alk. paper)
- Automorphic forms. 2. Automorphic funct ions. 3. Forms (Mathematics) I. Sarnak, Pe-
ter. II. Shahidi, F:reydoon.
QA353.A9A92 2007
51 5'.9-dc22 2006048036Copying and reprinting. Materia l in this book may be reproduced by any means for edu-
cationa l and scientific purposes without fee or permission with t h e exception of reproduction by
services that collect fees for d eli very of documents and provided that the customary acknowledg-
m ent of the source is given. T his consent d oes not extend to other kinds of copying for general
dist ribution, for ad vertising or promotional purposes, or for resale. Requests for p ermission for
commercial use of mate ri a l should b e addressed to the Acquisitions Department, American Math-
ematical Society, 201 C ha rles Street, Providence, Rhode Island 0 29 04-2294, USA. R equests can
a lso b e made by e-mail to reprint-permission©ams. org.
Excluded from these provisions is material in articles for which the author holds copyright. In
s uch cases, requests for p ermission to use or reprint should be addressed directly to the author(s).
(Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of
each article.)
© 2007 by the American Mathematical Society. A ll ri ghts reserved.
The American Mathem a tical Societ y retains all rights
except those granted to the United Stat es Government.
Copyright of individua l articles may revert to the public doma in 28 years
after publication. Contact the AMS for copyright status of individua l articles.
Printed in t he United States of A merica.
§ The paper used in t his book is acid-free and falls within t he guidelines
establis hed to ensure p erma ne nce and durability.
Visit the AMS home page at http: I /www.ams.org/
10 9 8 7 6 5 4 3 2 1 12 11 10 09 08 07