Overview

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).

Full Product Details

Author:   André Unterberger
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2000 ed.
Volume:   1742
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.840kg
ISBN:  

9783540678618

ISBN 10:   3540678611
Pages:   258
Publication Date:   28 August 2000
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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