André Unterberger

Quantization and Non-holomorphic Modular Forms (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 258
• Erscheinungstermin: 6. Mai 2007
• Englisch
• ISBN-13: 9783540446606
• Artikelnr.: 54010617

Autorenporträt

Universite de Reims, France [e-mail]

Inhaltsangabe

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.