Editorial Board of the Student Mathematical Library Gerald B. Folland Robin Forman Brad G. Osgood (Chair) John Stillwell Series Editor for the Park City Mathematics Institute John Polking Cover art courtesy of Karl Rubin, using MegaPOV, which is based on POV-Ray, both of which are open source, freely available software. 2000 Mathematics Subject Classification. Primary 14H52, 11G05 Secondary 11F03, 11G40. For additional information and updates on this book, visit www.ams.org/bookpages/stml-58 Library of Congress Cataloging-in-Publication Data Lozano-Robledo, ´ Alvaro, 1978– Elliptic curves, modular forms, and their L-functions / ´ Alvaro Lozano-Robledo. p. cm. (Student mathematical library v. 58. IAS/Park City mathemat- ical subseries) Includes bibliographical references and index. ISBN 978-0-8218-5242-2 (alk. paper) 1. Curves, Elliptic. 2. Forms, Modular. 3. L-functions. 4. Number theory. I. Title. QA567.2.E44L69 2010 516.3 52—dc22 2010038952 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904- 2294 USA. Requests can also be made by e-mail to reprint-permission@ams.org. c 2011 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 16 15 14 13 12 11
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