Contributions in Analytic and Algebraic Number Theory Festschrift fo
Contributions in Analytic and Algebraic Number Theory: Festschrift for S. J. Patterson is a collection of surveys and original work from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry.
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Springer Proceedings in Mathematics
The book series will feature volumes of selected contributions from workshops and conferences in all areas of current research activity in mathematics. Besides an overall evaluation, at the hands of the publisher, of the interest, scientific quality, and timeliness of each proposal, every individual contribution will be refereed to standards comparable to those of leading mathematics journals. It is hoped that this series will thus propose to the research community well-edited and authoritative reports on newest developments in the most interesting and promising areas of mathematical research today.
Valentin Blomer • Preda Mih˘ailescu Editors
Contributions in Analytic and Algebraic Number Theory Festschrift for S. J. Patterson
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Editors Valentin Blomer Mathematisches Institut Universit¨at G¨ottingen Bunsenstr. 3-5 37073 G¨ottingen, Germany [email protected]
Preda Mih˘ailescu Mathematisches Institut Universit¨at G¨ottingen Bunsenstr. 3-5 37073 G¨ottingen, Germany [email protected]
ISSN 2190-5614 e-ISSN 2190-5622 ISBN 978-1-4614-1218-2 e-ISBN 978-1-4614-1219-9 DOI 10.1007/978-1-4614-1219-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011941120 © 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)
Foreword
Few mathematicians in Germany in the last 30 years have influenced analytic number theory as much and as deeply as Samuel Patterson. His impressive genealogy is only one of the results of his active mathematical career. Many of the articles in this volume have been presented at the conference “Patterson 60++” at the University of G¨ottingen in July 2009 on the occasion of his 60th birthday. The conference featured four generations of mathematicians including Patterson’s children and grandchildren as well as his own advisor Prof. Alan F. Beardon who did not miss the opportunity to contribute an enjoyable and lively talk to the many mathematical birthday presents. The articles in this volume reflect Patterson’s manifold interests ranging from classical analytic number theory and exponential sums via automorphic forms on metaplectic groups to measure-theoretic as
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