Quantization and Non-holomorphic Modular Forms [[electronic resource] /] / by André Unterberger

• Autore: Unterberger André
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000
• Edizione: 1st ed. 2000.
• Descrizione fisica: 1 online resource (X, 258 p.)
• Disciplina: 510
• Soggetto topico: Number theory; Number Theory
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: 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.
• Sommario/riassunto: 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).
• Titolo autorizzato: Quantization and non-holomorphic modular forms
• ISBN: 3-540-44660-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466505803316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1742