Quantization and Non-holomorphic Modular Forms
This is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of
- PDF / 15,433,071 Bytes
- 251 Pages / 432 x 666 pts Page_size
- 70 Downloads / 226 Views
1742
Springer
Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Andre Unterberger
Quantization and Non-holomorphic Modular Forms
Springer
Author Andre Unterberger Mathernatiques (UPRESA 6056) Universite de Reims Moulin de la Housse, BP 1039 51687 Reims Cedex 2, France E-mail: andre.unterberger@univ-reimsJr
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Unterberger, Andre: Quantization and non-holomorphic modular forms I Andre Unterberger. Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics; 1742) ISBN 3-540-67861-1
Mathematics Subject Classification (2000): IIF03, l1L05, 35S99, 44A 12, 81S99 ISSN 0075-8434 ISBN 3-540-67861-1 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science-Business Media GmbH © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany TYpesetting: Camera-ready TEX output by the author SPIN: 10724305 41/3142-543210 - Printed on acid-free paper
Foreword: instructions for use
The aim of this manuscript is to bring together quantization theory and the theory of nou-holomorphic modular forms. It depends on a certain number of ideas from quantization theory, pseudodifferential analysis, partial differential equations and elementary harmonic analysis on one hand, from modular form theory on the other. As it adresses itself to two rather distinct possible audiences, we include the present foreword, as an answer to the question "who might be interested in reading what ?". Still, let us stress that, from our point of view, trade between mathematical disciplines should be conducted on a reciprocal basis: we thus hope that some number theorists may view our present investigations not only, or even mostly, as a - well-founded or not - claim that pseudodifferential analysis has something to contribute to modular form theory but, also, as an invitation to join a possibly unfamiliar playground. That the game is far from being over will be shown at the end of this foreword. The reader interested in modular form theory, but not in motivations from quantization theory, might be advised to jump from the introduction to section 7, in which the Rankin-Selberg unfolding method is extended to some fair degree: thanks to the hyperfunction concept, the extended method permits to recover the Roe
Data Loading...
