LEADER 03621nam 22005895 450 001 9910146318103321 005 20200702174754.0 010 $a3-540-44660-5 024 7 $a10.1007/BFb0104036 035 $a(CKB)1000000000437272 035 $a(SSID)ssj0000326027 035 $a(PQKBManifestationID)12116408 035 $a(PQKBTitleCode)TC0000326027 035 $a(PQKBWorkID)10264783 035 $a(PQKB)10349240 035 $a(DE-He213)978-3-540-44660-6 035 $a(MiAaPQ)EBC6283153 035 $a(MiAaPQ)EBC5590980 035 $a(Au-PeEL)EBL5590980 035 $a(OCoLC)1066187594 035 $a(PPN)155169572 035 $a(EXLCZ)991000000000437272 100 $a20121227d2000 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aQuantization and Non-holomorphic Modular Forms /$fby André Unterberger 205 $a1st ed. 2000. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000. 215 $a1 online resource (X, 258 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1742 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-67861-1 320 $aIncludes bibliographical references and indexes. 327 $aDistributions 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. 330 $aThis is a new approach to the theory of non-holomorphic modular forms, based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin-Selberg method so as to apply it to the calculation of the Roelcke-Selberg decomposition of the product of two Eisenstein series, one lets Maass cusp-forms appear as residues of simple, Eisenstein-like, series. Other results, based on quantization theory, include a reinterpretation of the Lax-Phillips scattering theory for the automorphic wave equation, in terms of distributions on R2 automorphic with respect to the linear action of SL(2,Z). 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1742 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a510 700 $aUnterberger$b André$4aut$4http://id.loc.gov/vocabulary/relators/aut$0351381 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146318103321 996 $aQuantization and non-holomorphic modular forms$978812 997 $aUNINA