Archimedean Zeta Integrals for CL(3) x GL(2) / / Miki Hirano, Taku Ishii, Tadashi Miyazaki

• Autore: Hirano Miki
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (136 pages)
• Disciplina: 515/.55; 515.55
• Soggetto topico: Coulomb 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
• Classificazione: 11F7011F3022E46
• Altri autori: IshiiTaku MiyazakiTadashi
• Nota di contenuto: 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> -- - ₂' -- 10.7. The calculation in the case - ₁'> -- 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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Archimedean Zeta Integrals for CL(3) x GL(2)
• ISBN: 9781470471668; 1470471663
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910965481803321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society