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[null,"1.","Record Nr.",null,"UNINA9910965481803321"]
[null,null,"Autore",null,"Hirano Miki"]
[null,null,"Titolo",null,"Archimedean Zeta Integrals for CL(3) x GL(2) / / Miki Hirano, Taku Ishii, Tadashi Miyazaki"]
[null,null,"Pubbl/distr/stampa",null,"Providence : , : American Mathematical Society, , 2022"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"9781470471668"]
[{"$nulls":4},"1470471663"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (136 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; v.278"]
[null,null,"Classificazione",null,"11F7011F3022E46"]
[null,null,"Disciplina",null,"515/.55"]
[{"$nulls":4},"515.55"]
[null,null,"Soggetti",null,"Coulomb functions"]
[{"$nulls":4},"Riemann integral"]
[{"$nulls":4},"Functions, Zeta"]
[{"$nulls":4},"Automorphic forms"]
[{"$nulls":4},"Number theory -- Discontinuous groups and automorphic forms -- Representation-theoretic methods; automorphic representations over local and global fields"]
[{"$nulls":4},"Number theory -- Discontinuous groups and automorphic forms -- Fourier coefficients of automorphic forms"]
[{"$nulls":4},"Topological groups, Lie groups -- Lie groups -- Semisimple Lie groups and their representations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Cover -- Title page -- Introduction -- Acknowledgments -- Part 1. Whittaker functions -- Chapter 1. Basic objects -- 1.1. Notation -- 1.2. Groups and algebras -- 1.3. Whittaker functions -- 1.4. Capelli elements -- 1.5. The gamma function and the Bessel functions -- 1.6. Special functions of two variables -- Chapter 2. Preliminaries for   ( ,\\bR) -- 2.1. Generalized principal series representations -- 2.2. The elements of \\g_{\\bC} and  (\\g_{\\bC}) -- 2.3. The eigenvalues of generators of  (\\g_{\\bC}) -- Chapter 3. Whittaker functions on   (2,\\bR) -- 3.1. Representations of  (2) -- 3.2. Principal series representations -- 3.3. Principal series Whittaker functions -- 3.4. Essentially discrete series Whittaker functions -- Chapter 4. Whittaker functions on   (3,\\bR) -- 4.1. Representations of  (3) -- 4.2. Principal series representations -- 4.3. Principal series Whittaker functions at scalar  -"]
[{"$nulls":4},"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)."]
[{"$nulls":4},"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."]
[null,null,null,"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\"--"]