01045nam a2200265 i 450099100246642970753620020508200700.0980515s1997 it ||| | ita 882211891Xb11013424-39ule_instPARLA163104ExLDip.to Filosofiaita193Partesana, Ezio538786Critica del non vero :per una teoria dell'interpretazione in Th.W. Adorno /Ezio PartesanaFirenze :Nuova Italia,1997x, 236 p. ;23 cm.Pubblicazioni della Facoltà di Lettere e Filosofia dell'Università degli Studi di Milano. Sezione di Filologia classica ;25Adorno, Theodor W..b1101342423-02-1728-06-02991002466429707536LE005 193 ADO01. PAR01. 0112005000018480le005-E0.00-l- 00000.i1113150028-06-02Critica del non vero861463UNISALENTOle00501-01-98ma -itait 0105970nam 22006613 450 991096548180332120231110223243.097814704716681470471663(MiAaPQ)EBC29379019(Au-PeEL)EBL29379019(CKB)24267686200041(OCoLC)1336953688(EXLCZ)992426768620004120220721d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierArchimedean Zeta Integrals for CL(3) x GL(2) /Miki Hirano, Taku Ishii, Tadashi Miyazaki1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (136 pages)Memoirs of the American Mathematical Society ;v.278Print version: Hirano, Miki Archimedean Zeta Integrals for Providence : American Mathematical Society,c2022 9781470452773 Cover -- Title page -- Introduction -- Acknowledgments -- Part 1. Whittaker functions -- Chapter 1. Basic objects -- 1.1. Notation -- 1.2. Groups and algebras -- 1.3. Whittaker functions -- 1.4. Capelli elements -- 1.5. The gamma function and the Bessel functions -- 1.6. Special functions of two variables -- Chapter 2. Preliminaries for ( ,\bR) -- 2.1. Generalized principal series representations -- 2.2. The elements of \g_{\bC} and (\g_{\bC}) -- 2.3. The eigenvalues of generators of (\g_{\bC}) -- Chapter 3. Whittaker functions on (2,\bR) -- 3.1. Representations of (2) -- 3.2. Principal series representations -- 3.3. Principal series Whittaker functions -- 3.4. Essentially discrete series Whittaker functions -- Chapter 4. Whittaker functions on (3,\bR) -- 4.1. Representations of (3) -- 4.2. Principal series representations -- 4.3. Principal series Whittaker functions at scalar -types -- 4.4. Principal series Whittaker functions at 3 dimensional -types -- 4.5. Generalized principal series representations -- 4.6. Generalized principal series Whittaker functions -- Chapter 5. Preliminaries for ( ,\bC) -- 5.1. Principal series representations -- 5.2. The elements of \g_{\bC} and (\g_{\bC}) -- 5.3. The eigenvalues of generators of (\g_{\bC}) -- Chapter 6. Whittaker functions on (2,\bC) -- 6.1. Representations of (2) -- 6.2. Principal series representations -- 6.3. Principal series Whittaker functions -- Chapter 7. Whittaker functions on (3,\bC) -- 7.1. Representations of (3) -- 7.2. Principal series representations -- 7.3. Principal series Whittaker functions -- Part 2. Archimedean zeta integrals for (3)× (2) -- Chapter 8. Preliminaries -- 8.1. The aim of Part 2 -- 8.2. Some formulas for the calculation -- Chapter 9. The local zeta integrals for (3,\bR)× (2,\bR) -- 9.1. The local Langlands correspondence for ( ,\bR).9.2. Preparations for (2)-modules -- 9.3. Whittaker functions on (2,\bR) -- 9.4. Whittaker functions on (3,\bR) -- 9.5. The local zeta integrals for (3,\bR)× (2,\bR) -- 9.6. The calculation for '= _{( ₁', ₂')}⊠ _{( ₂', ₂')} -- 9.7. The calculation for '= _{( ₁',1)}⊠ _{( ₂',0)} -- 9.8. The calculation for '= _{( ', ')} -- Chapter 10. The local zeta integrals for (3,\bC)× (2,\bC) -- 10.1. The local Langlands correspondence for ( ,\bC) -- 10.2. Preparations for (2)-modules -- 10.3. Whittaker functions on (2,\bC) -- 10.4. Whittaker functions on (3,\bC) -- 10.5. The local zeta integrals for (3,\bC)× (2,\bC) -- 10.6. The calculation in the case ₂&gt -- - ₂' -- 10.7. The calculation in the case - ₁'&gt -- ₂ -- 10.8. The calculation in the case - ₂'≥ ₂≥- ₁' -- Appendix A. Archimedean zeta integrals for (2)× ( ) ( =1,2) -- A.1. The local zeta integrals for (2,\bR)× (1,\bR) -- A.2. The local zeta integrals for (2,\bR)× (2,\bR) -- A.3. The local zeta integrals for (2,\bC)× (1,\bC) -- A.4. The local zeta integrals for (2,\bC)× (2,\bC) -- Bibliography -- Back Cover."In this article, we give explicit formulas of archimedean Whittaker functions on GL(3) and GL(2). Moreover, we apply those to the calculation of archimedean zeta integrals for GL(3) x GL(2), and show that the zeta integral for appropriate Whittaker functions is equal to the associated L-factors"--Provided by publisher.Memoirs of the American Mathematical Society Coulomb functionsRiemann integralFunctions, ZetaAutomorphic formsNumber theory -- Discontinuous groups and automorphic forms -- Representation-theoretic methods; automorphic representations over local and global fieldsmscNumber theory -- Discontinuous groups and automorphic forms -- Fourier coefficients of automorphic formsmscTopological groups, Lie groups -- Lie groups -- Semisimple Lie groups and their representationsmscCoulomb functions.Riemann integral.Functions, Zeta.Automorphic forms.Number theory -- Discontinuous groups and automorphic forms -- Representation-theoretic methods; automorphic representations over local and global fields.Number theory -- Discontinuous groups and automorphic forms -- Fourier coefficients of automorphic forms.Topological groups, Lie groups -- Lie groups -- Semisimple Lie groups and their representations.515/.55515.5511F7011F3022E46mscHirano Miki1801825Ishii Taku1801826Miyazaki Tadashi1801827MiAaPQMiAaPQMiAaPQBOOK9910965481803321Archimedean Zeta Integrals for CL(3) x GL(2)4347225UNINA