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Quantization and Non-holomorphic Modular Forms

  • Authors
  • André Unterberger

Part of the Lecture Notes in Mathematics book series (LNM, volume 1742)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. André Unterberger
    Pages 1-9
  3. André Unterberger
    Pages 17-23
  4. André Unterberger
    Pages 33-44
  5. André Unterberger
    Pages 69-75
  6. André Unterberger
    Pages 91-96
  7. André Unterberger
    Pages 119-130
  8. André Unterberger
    Pages 149-161
  9. André Unterberger
    Pages 163-176
  10. André Unterberger
    Pages 177-190
  11. André Unterberger
    Pages 231-246
  12. Back Matter
    Pages 248-253

About this book

Introduction

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 the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action of SL(2,Z).

Keywords

Boundary value problem Kloosterman series Lax-Phillips theory Non-holomorphic modular forms Rankin-Cohen products automorphic distributions scattering theory wave equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0104036
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67861-8
  • Online ISBN 978-3-540-44660-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site