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Archimedean Zeta Integrals for CL(3) x GL(2) / / Miki Hirano, Taku Ishii, Tadashi Miyazaki
| Archimedean Zeta Integrals for CL(3) x GL(2) / / Miki Hirano, Taku Ishii, Tadashi Miyazaki |
| Autore | Hirano Miki |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (136 pages) |
| Disciplina |
515/.55
515.55 |
| Altri autori (Persone) |
IshiiTaku
MiyazakiTadashi |
| Collana | Memoirs of the American Mathematical Society |
| 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 |
| ISBN |
9781470471668
1470471663 |
| Classificazione | 11F7011F3022E46 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910965481803321 |
Hirano Miki
|
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Asymptotic forms of Whittaker's confluent hypergeometric functions / / A. Erdélyi, C.A. Swanson
| Asymptotic forms of Whittaker's confluent hypergeometric functions / / A. Erdélyi, C.A. Swanson |
| Autore | Erdélyi Arthur |
| Pubbl/distr/stampa | Providence, R.I. : , : American Mathematical Society, , 1957 |
| Descrizione fisica | 1 online resource (60 pages) |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Airy functions
Coulomb functions Hypergeometric functions |
| ISBN | 0-8218-9967-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""1. Introduction""; ""2. Confluent hypergeometric functions""; ""3. Bessel functions""; ""4. Airy functions""; ""5. The Bessel comparison functions""; ""6. The functions U and T""; ""7. Asymptotic forms for the functions u[sub(r)] and u[sub(r)]'""; ""8. The Airy comparison functions""; ""9. Asymptotic forms for the functions v[sub(r)] and v[sub(r)]'""; ""10. Asymptotic forms for Whittaker functions""; ""11. Asymptotic forms for Coulomb wave functions""; ""12. Simplified asymptotic forms for restricted x-intervals""; ""References"" |
| Altri titoli varianti | Whittaker's confluent hypergeometric functions |
| Record Nr. | UNINA-9910788769303321 |
|
Erdélyi Arthur
|
||
| Providence, R.I. : , : American Mathematical Society, , 1957 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotic forms of Whittaker's confluent hypergeometric functions / / A. Erdélyi, C.A. Swanson
| Asymptotic forms of Whittaker's confluent hypergeometric functions / / A. Erdélyi, C.A. Swanson |
| Autore | Erdélyi Arthur |
| Pubbl/distr/stampa | Providence, R.I. : , : American Mathematical Society, , 1957 |
| Descrizione fisica | 1 online resource (60 pages) |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Airy functions
Coulomb functions Hypergeometric functions |
| ISBN | 0-8218-9967-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Table of Contents""; ""1. Introduction""; ""2. Confluent hypergeometric functions""; ""3. Bessel functions""; ""4. Airy functions""; ""5. The Bessel comparison functions""; ""6. The functions U and T""; ""7. Asymptotic forms for the functions u[sub(r)] and u[sub(r)]'""; ""8. The Airy comparison functions""; ""9. Asymptotic forms for the functions v[sub(r)] and v[sub(r)]'""; ""10. Asymptotic forms for Whittaker functions""; ""11. Asymptotic forms for Coulomb wave functions""; ""12. Simplified asymptotic forms for restricted x-intervals""; ""References"" |
| Altri titoli varianti | Whittaker's confluent hypergeometric functions |
| Record Nr. | UNINA-9910828811703321 |
|
Erdélyi Arthur
|
||
| Providence, R.I. : , : American Mathematical Society, , 1957 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon
| Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon |
| Autore | Gon Yasuro |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina |
510 s
512/.73 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Coulomb functions
Forms, Modular Representations of groups |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0331-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1. Introduction""; ""Chapter 2. Generalized Whittaker functions and representation theory of SU(2,2)""; ""2. Definition of the generalized Whittaker functions""; ""3. Structure theory for SU(2,2) and its Lie algebra""; ""4. Representations of K""; ""5. Irreducible SU(Î?)-modules""; ""6. Explicit description of Whittaker functions""; ""7. Radial part of the shift operators""; ""Chapter 3. Generalized Whittaker functions for P[sub(J)] principal series representations""; ""8. Generalized Whittaker functions for P[sub(J)]-principal series""
""Chapter 4. Generalized Whittaker functions for the discrete series representations""""9. Generalized Whittaker functions for the discrete series representations""; ""10. Generalized Whittaker functions for the holomorphic discrete series representations""; ""11. Generalized Whittaker functions for the large discrete series representations""; ""12. Generalized Whittaker functions for the middle discrete representations""; ""13. Generalized Whittaker functions for the middle discrete series associated with definite H[sub(Î?)]"" ""14. Generalized Whittaker functions for the middle discrete series associated with indefinite H[sub(Î?)]""""Bibliography"" |
| Record Nr. | UNINA-9910479980603321 |
|
Gon Yasuro
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon
| Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon |
| Autore | Gon Yasuro |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina |
510 s
512/.73 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Coulomb functions
Forms, Modular Representations of groups |
| ISBN | 1-4704-0331-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1. Introduction""; ""Chapter 2. Generalized Whittaker functions and representation theory of SU(2,2)""; ""2. Definition of the generalized Whittaker functions""; ""3. Structure theory for SU(2,2) and its Lie algebra""; ""4. Representations of K""; ""5. Irreducible SU(Î?)-modules""; ""6. Explicit description of Whittaker functions""; ""7. Radial part of the shift operators""; ""Chapter 3. Generalized Whittaker functions for P[sub(J)] principal series representations""; ""8. Generalized Whittaker functions for P[sub(J)]-principal series""
""Chapter 4. Generalized Whittaker functions for the discrete series representations""""9. Generalized Whittaker functions for the discrete series representations""; ""10. Generalized Whittaker functions for the holomorphic discrete series representations""; ""11. Generalized Whittaker functions for the large discrete series representations""; ""12. Generalized Whittaker functions for the middle discrete representations""; ""13. Generalized Whittaker functions for the middle discrete series associated with definite H[sub(Î?)]"" ""14. Generalized Whittaker functions for the middle discrete series associated with indefinite H[sub(Î?)]""""Bibliography"" |
| Record Nr. | UNINA-9910788845303321 |
|
Gon Yasuro
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon
| Generalized Whittaker functions on SU(2,2) with respect to the Siegel parabolic subgroup / / Yasuro Gon |
| Autore | Gon Yasuro |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2002] |
| Descrizione fisica | 1 online resource (130 p.) |
| Disciplina |
510 s
512/.73 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Coulomb functions
Forms, Modular Representations of groups |
| ISBN | 1-4704-0331-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""1. Introduction""; ""Chapter 2. Generalized Whittaker functions and representation theory of SU(2,2)""; ""2. Definition of the generalized Whittaker functions""; ""3. Structure theory for SU(2,2) and its Lie algebra""; ""4. Representations of K""; ""5. Irreducible SU(Î?)-modules""; ""6. Explicit description of Whittaker functions""; ""7. Radial part of the shift operators""; ""Chapter 3. Generalized Whittaker functions for P[sub(J)] principal series representations""; ""8. Generalized Whittaker functions for P[sub(J)]-principal series""
""Chapter 4. Generalized Whittaker functions for the discrete series representations""""9. Generalized Whittaker functions for the discrete series representations""; ""10. Generalized Whittaker functions for the holomorphic discrete series representations""; ""11. Generalized Whittaker functions for the large discrete series representations""; ""12. Generalized Whittaker functions for the middle discrete representations""; ""13. Generalized Whittaker functions for the middle discrete series associated with definite H[sub(Î?)]"" ""14. Generalized Whittaker functions for the middle discrete series associated with indefinite H[sub(Î?)]""""Bibliography"" |
| Record Nr. | UNINA-9910818970403321 |
|
Gon Yasuro
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2002] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
