03271nam 2200673 450 99646648350331620220304061723.03-540-47880-910.1007/BFb0078125(CKB)1000000000437551(SSID)ssj0000323055(PQKBManifestationID)12131997(PQKBTitleCode)TC0000323055(PQKBWorkID)10296390(PQKB)10156408(DE-He213)978-3-540-47880-5(MiAaPQ)EBC5610545(Au-PeEL)EBL5610545(OCoLC)1078996596(MiAaPQ)EBC6842848(Au-PeEL)EBL6842848(OCoLC)1058097130(PPN)155169823(EXLCZ)99100000000043755120220304d1987 uy 0engurnn|008mamaatxtccrExplicit constructions of automorphic L-functions /Stephen Gelbart, Ilya Piatetski-Shapiro, Stephen Rallis1st ed. 1987.Berlin :Springer-Verlag,[1987]©19871 online resource (VIII, 156 p.) Lecture notes in mathematics ;1254Bibliographic Level Mode of Issuance: Monograph3-540-17848-1 Includes bibliographical references and indexes.Contents: 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.The 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.Lecture notes in mathematics (Springer-Verlag) ;1254.L-functionsAutomorphic formsRepresentations of groupsL-functions.Automorphic forms.Representations of groups.512.73Gelbart Stephen S.1946-45743Pi︠a︡tet︠s︡kiĭ-Shapiro I. I(Ilʹi︠a︡ Iosifovich),1929-2009,Rallis Stephen1942-MiAaPQMiAaPQMiAaPQBOOK996466483503316Explicit constructions of automorphic L-functions262370UNISA