03621nam 22005895 450 991014631810332120200702174754.03-540-44660-510.1007/BFb0104036(CKB)1000000000437272(SSID)ssj0000326027(PQKBManifestationID)12116408(PQKBTitleCode)TC0000326027(PQKBWorkID)10264783(PQKB)10349240(DE-He213)978-3-540-44660-6(MiAaPQ)EBC6283153(MiAaPQ)EBC5590980(Au-PeEL)EBL5590980(OCoLC)1066187594(PPN)155169572(EXLCZ)99100000000043727220121227d2000 u| 0engurnn|008mamaatxtccrQuantization and Non-holomorphic Modular Forms /by André Unterberger1st ed. 2000.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2000.1 online resource (X, 258 p.) Lecture Notes in Mathematics,0075-8434 ;1742Bibliographic Level Mode of Issuance: Monograph3-540-67861-1 Includes bibliographical references and indexes.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.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).Lecture Notes in Mathematics,0075-8434 ;1742Number theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Number theory.Number Theory.510Unterberger Andréauthttp://id.loc.gov/vocabulary/relators/aut351381MiAaPQMiAaPQMiAaPQBOOK9910146318103321Quantization and non-holomorphic modular forms78812UNINA