Quantization and non-holomorphic modular forms
Author(s)
Bibliographic Information
Quantization and non-holomorphic modular forms
(Lecture notes in mathematics, 1742)
Springer, c2000
Available at 75 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Includes bibliographical references (p. [251]-253) and indexes
Description and Table of Contents
Description
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).
Table of Contents
1. Introduction 2. Distributions associated with the non-unitary principal series 3. Modular distributions 4. The principal series of SL(2,R) and the Radon transform 5. Another look at the composition of Weyl symbols 6. The Roelcke-Selberg decomposition and the Radon transform 7. Recovering the Roelcke-Selberg coefficients of a function in L2 of the fundamental domain 8. The 'product' of two Eisenstein distributions 9. The Roelcke-Selberg expansion of the product of two Eisenstein series : the continuous part 10. A digression on Kloosterman sums 11. The Roelcke-Selberg expansion of the product of two Eisenstein series : the discrete part 12. The expansion of the Poisson bracket of two Eisenstein series 13. Automorphic distributions on R2 14. The Hecke decomposition of products or Poisson brackets of two Eisenstein series 15. A generating series of sorts for Maass cusp-forms 16. Some arithmetic distributions 17. Quantization, products and Poisson brackets 18. Moving to the forward light-cone: the Lax- Phillips theory revisited 19. Automorphic functions associated with quadratic PSL(2,Z)-orbits in P1(R) 20. Quadratic orbits: a dual problem Index of notations: page 1 Index of notations: page 2 Subject index References
by "Nielsen BookData"