LEADER 03036nam 2200637 450 001 996466515403316 005 20220910125547.0 010 $a3-540-47761-6 024 7 $a10.1007/BFb0077894 035 $a(CKB)1000000000437560 035 $a(SSID)ssj0000324407 035 $a(PQKBManifestationID)12080848 035 $a(PQKBTitleCode)TC0000324407 035 $a(PQKBWorkID)10305402 035 $a(PQKB)10032975 035 $a(DE-He213)978-3-540-47761-7 035 $a(MiAaPQ)EBC5578204 035 $a(Au-PeEL)EBL5578204 035 $a(OCoLC)1066178815 035 $a(MiAaPQ)EBC6841939 035 $a(Au-PeEL)EBL6841939 035 $a(OCoLC)1292362838 035 $a(PPN)155192043 035 $a(EXLCZ)991000000000437560 100 $a20220910d1987 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aL functions and the oscillator representation /$fStephen Rallis 205 $a1st ed. 1987. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1987] 210 4$dİ1987 215 $a1 online resource (XVI, 240 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1245 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-17694-2 311 $a3-540-17694-2 327 $aNotation and preliminaries -- Special Eisenstein series on orthogonal groups -- Siegel formula revisited -- Inner product formulae -- Siegel formula ? Compact case -- Local l-factors -- Global theory. 330 $aThese notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the nonvanishing of a *F2 correspondence by computing the Petersson inner product of a *F2 lift from *F1 to O(Q) is considered. This product can be expressed as the special value of an L-function (associated to the standard representation of the L-group of *F1) times a finite number of local Euler factors (measuring whether a given local representation occurs in a given oscillator representation). The key ideas used in proving this are (i) new Rankin integral representations of standard L-functions, (ii) see-saw dual reductive pairs and (iii) Siegel-Weil formula. The book addresses readers who specialize in the theory of automorphic forms and L-functions and the representation theory of Lie groups. N. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1245 606 $aRepresentations of groups$vCongresses 606 $aNumber theory 615 0$aRepresentations of groups 615 0$aNumber theory. 676 $a512.7 686 $a10D05$2msc 700 $aRallis$b Stephen$f1942-$056906 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466515403316 996 $aL-functions and the oscillator representation$978526 997 $aUNISA