LEADER 03271nam 2200673 450 001 996466483503316 005 20220304061723.0 010 $a3-540-47880-9 024 7 $a10.1007/BFb0078125 035 $a(CKB)1000000000437551 035 $a(SSID)ssj0000323055 035 $a(PQKBManifestationID)12131997 035 $a(PQKBTitleCode)TC0000323055 035 $a(PQKBWorkID)10296390 035 $a(PQKB)10156408 035 $a(DE-He213)978-3-540-47880-5 035 $a(MiAaPQ)EBC5610545 035 $a(Au-PeEL)EBL5610545 035 $a(OCoLC)1078996596 035 $a(MiAaPQ)EBC6842848 035 $a(Au-PeEL)EBL6842848 035 $a(OCoLC)1058097130 035 $a(PPN)155169823 035 $a(EXLCZ)991000000000437551 100 $a20220304d1987 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aExplicit constructions of automorphic L-functions /$fStephen Gelbart, Ilya Piatetski-Shapiro, Stephen Rallis 205 $a1st ed. 1987. 210 1$aBerlin :$cSpringer-Verlag,$d[1987] 210 4$dİ1987 215 $a1 online resource (VIII, 156 p.) 225 1 $aLecture notes in mathematics ;$v1254 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-17848-1 320 $aIncludes bibliographical references and indexes. 327 $aContents: L-Functions for the Classical Groups -- L-Functions for G GL(n): Basic Identities and the Euler Product Expansion. The Local Functional Equation -- General Index -- Index of Notation. 330 $aThe goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1254. 606 $aL-functions 606 $aAutomorphic forms 606 $aRepresentations of groups 615 0$aL-functions. 615 0$aAutomorphic forms. 615 0$aRepresentations of groups. 676 $a512.73 700 $aGelbart$b Stephen S.$f1946-$045743 702 $aPi?a?tet?s?kii?-Shapiro$b I. I$g(Il?i?a? Iosifovich),$f1929-2009, 702 $aRallis$b Stephen$f1942- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466483503316 996 $aExplicit constructions of automorphic L-functions$9262370 997 $aUNISA