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Quantization and Non-holomorphic Modular Forms

  • Book
  • © 2000

Overview

Authors:
  1. André Unterberger
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1742)

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • André Unterberger
    Pages 1-9

  3. Distributions associated with the non-unitary principal series

    • André Unterberger
    Pages 11-15

  4. Modular distributions

    • André Unterberger
    Pages 17-23

  5. The principal series of SL(2, ℝ) and the Radon transform

    • André Unterberger
    Pages 25-31

  6. Another look at the composition of Weyl symbols

    • André Unterberger
    Pages 33-44

  7. The Roelcke-Selberg decomposition and the Radon transform

    • André Unterberger
    Pages 45-59

  8. Recovering the Roelcke-Selberg coefficients of a function in L 2(Γ∖Π)

    • André Unterberger
    Pages 61-68

  9. The “product” of two Eisenstein distributions

    • André Unterberger
    Pages 69-75

  10. The roelcke-selberg expansion of the product of two eisenstein series: the continuous part

    • André Unterberger
    Pages 77-90

  11. A digression on kloosterman sums

    • André Unterberger
    Pages 91-96

  12. The roelcke-selberg expansion of the product of two eisenstein series: the discrete part

    • André Unterberger
    Pages 97-109

  13. The expansion of the poisson bracket of two eisenstein series

    • André Unterberger
    Pages 111-117

  14. Automorphic distributions on ℝ2

    • André Unterberger
    Pages 119-130

  15. The Hecke decomposition of products or Poisson brackets of two Eisenstein series

    • André Unterberger
    Pages 131-147

  16. A generating series of sorts for Maass cusp-forms

    • André Unterberger
    Pages 149-161

  17. Some arithmetic distributions

    • André Unterberger
    Pages 163-176

  18. Quantization, products and Poisson brackets

    • André Unterberger
    Pages 177-190

  19. Moving to the forward light-cone: the Lax-Phillips theory revisited

    • André Unterberger
    Pages 191-212

  20. Automorphic functions associated with quadratic PSL(2, ℤ)-orbits in P 1(ℝ)

    • André Unterberger
    Pages 213-230
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Keywords

About this book

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).

Bibliographic Information

  • Book Title: Quantization and Non-holomorphic Modular Forms

  • Authors: André Unterberger

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0104036

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-67861-8Published: 28 August 2000

  • eBook ISBN: 978-3-540-44660-6Published: 06 May 2007

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 258

  • Topics: Number Theory

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