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Quantization and Non-holomorphic Modular Forms de André Unterberger

Quantization and Non-holomorphic Modular Forms: Lecture Notes in Mathematics, cartea 1742

Autor André Unterberger
en Limba Engleză Paperback – 28 aug 2000
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).
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Specificații

ISBN-13: 9783540678618
ISBN-10: 3540678611
Pagini: 268
Ilustrații: X, 258 p.
Dimensiuni: 155 x 233 x 15 mm
Greutate: 0.41 kg
Ediția:2000
Editura: Springer
Colecția Lecture Notes in Mathematics
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Distributions associated with the non-unitary principal series.- Modular distributions.- The principal series of SL(2, ?) and the Radon transform.- Another look at the composition of Weyl symbols.- The Roelcke-Selberg decomposition and the Radon transform.- Recovering the Roelcke-Selberg coefficients of a function in L 2(???).- The “product” of two Eisenstein distributions.- The roelcke-selberg expansion of the product of two eisenstein series: the continuous part.- A digression on kloosterman sums.- The roelcke-selberg expansion of the product of two eisenstein series: the discrete part.- The expansion of the poisson bracket of two eisenstein series.- Automorphic distributions on ?2.- The Hecke decomposition of products or Poisson brackets of two Eisenstein series.- A generating series of sorts for Maass cusp-forms.- Some arithmetic distributions.- Quantization, products and Poisson brackets.- Moving to the forward light-cone: the Lax-Phillips theory revisited.- Automorphic functions associated with quadratic PSL(2, ?)-orbits in P 1(?).- Quadratic orbits: a dual problem.