Number Theory, Analysis and Geometry In Memory of Serge Lang
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amoun
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Dorian Goldfeld • Jay Jorgenson • Peter Jones Dinakar Ramakrishnan • Kenneth A. Ribet John Tate Editors
Number Theory, Analysis and Geometry In Memory of Serge Lang
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Editors Dorian Goldfeld Department of Mathematics Columbia University New York, NY 10027 USA [email protected]
Jay Jorgenson Department of Mathematics City University of New York New York, NY 10031 USA [email protected]
Peter Jones Department of Mathematics Yale University New Haven, CT 06520 USA [email protected]
Dinakar Ramakrishnan Department of Mathematics California Institute of Technology Pasadena, CA 91125 USA [email protected]
Kenneth A. Ribet Department of Mathematics University of California at Berkeley Berkeley, CA 94720 USA [email protected]
John Tate Department of Mathematics Harvard University Cambridge, MA 02138 USA [email protected]
ISBN 978-1-4614-1259-5 e-ISBN 978-1-4614-1260-1 DOI 10.1007/978-1-4614-1260-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011941121 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Serge Lang (Photo provided courtesy of Kenneth A. Ribet.)
Preface
Serge Lang was an iconic figure in mathematics, both for his own important work and, perhaps even more crucially, for the indelible impact he left on the field, and on his students and colleagues. It would be difficult to find a mathematician who came of age in the past forty years, who had not been exposed to Serge’s articles, monographs, and textbooks. Serge’s writing shaped the mathematical perspectives of all who came in contact with them. Many were challenged by the glimpses of open problems and conjectures that Serge interweaved with his expositions of established subjects. Serge’s exposition invariably transcended our discipline’s preference for brevity and perfection, which often obscures the intuition underlying the subject. Serge was never one to conform. One of Serge’s uplifting qualities was his openness to new areas of mathematics and his concurrent willingness, even eagerness, to learn novel concepts and techniques. He was constantly reinventing himself, while sharing his accumulated wisdom with students and young mathematicians. Over the course of his career, he t
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