Pseudodifferential Operators with Automorphic Symbols
The main results of this book combine pseudodifferential analysis with modular form and L-function theory, with the help of explicit spectral-theoretic calculations. The starting point is a notion of modular distribution in the plane, which will be new to
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André Unterberger
Pseudodifferential Operators with Automorphic Symbols
Pseudo-Differential Operators Theory and Applications Vol. 11
Managing Editor M.W. Wong (York University, Canada)
Editorial Board Luigi Rodino (Università di Torino, Italy) Bert-Wolfgang Schulze (Universität Potsdam, Germany) Johannes Sjöstrand (Université de Bourgogne, Dijon, France) Sundaram Thangavelu (Indian Institute of Science at Bangalore, India) Maciej Zworski (University of California at Berkeley, USA)
Pseudo-Differential Operators: Theory and Applications is a series of moderately priced graduate-level textbooks and monographs appealing to students and experts alike. Pseudo-differential operators are understood in a very broad sense and include such topics as harmonic analysis, PDE, geometry, mathematical physics, microlocal analysis, time-frequency analysis, imaging and computations. Modern trends and novel applications in mathematics, natural sciences, medicine, scientific computing, and engineering are highlighted.
André Unterberger
Pseudodifferential Operators with Automorphic Symbols
André Unterberger Université de Reims Laboratoire de Mathématiques Reims, France
ISSN 2297-0355 ISSN 2297-0363 (electronic) Pseudo-Differential Operators ISBN 978-3-319-18656-6 ISBN 978-3-319-18657-3 (eBook) DOI 10.1007/978-3-319-18657-3 Library of Congress Control Number: 2015943692 Mathematics Subject Classification (2010): 11F03, 11F37, 47G30 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.birkhauser-science.com)
Preface The present book, just as some of its forerunners, grew out of the author’s desire to find a different approach to analytic number theory, certainly one of the more aesthetically satisfying branches of mathematics: this is especially true so far as modu
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