Automorphic forms on SL2(R):
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1997
|
| Series: | Cambridge tracts in mathematics
130 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book |
| Physical Description: | 1 Online-Ressource (x, 192 Seiten) |
| ISBN: | 9780511896064 |
| DOI: | 10.1017/CBO9780511896064 |
Staff View
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| 505 | 8 | |a Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: -- 1. Prerequisites and notation -- 2. Review of SL2(R), differential operators, convolution -- 3. Action of G on X, discrete subgroups of G, fundamental domains -- 4. The unit disc model -- Part II. Automorphic Forms and Cusp Forms: -- 5. Growth conditions, automorphic forms -- 6. Poincare series -- 7. Constant term:the fundamental estimate -- 8. Finite dimensionality of the space of automorphic forms of a given type -- 9. Convolution operators on cuspidal functions -- Part III. Eisenstein Series: -- 10. Definition and convergence of Eisenstein series -- 11. Analytic continuation of the Eisenstein series -- 12. Eisenstein series and automorphic forms orthogonal to cusp forms -- Part IV. Spectral Decomposition and Representations: -- 13. Spectral decomposition of L2(G\G)m with respect to C -- 14. Generalities on representations of G -- 15. Representations of SL2(R) -- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum -- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum -- 18. Concluding remarks | |
| 520 | |a This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book | ||
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Record in the Search Index
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| any_adam_object | |
| author | Borel, Armand |
| author_facet | Borel, Armand |
| author_role | aut |
| author_sort | Borel, Armand |
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| building | Verbundindex |
| bvnumber | BV043942179 |
| classification_rvk | SK 180 SK 750 |
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| contents | Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: -- 1. Prerequisites and notation -- 2. Review of SL2(R), differential operators, convolution -- 3. Action of G on X, discrete subgroups of G, fundamental domains -- 4. The unit disc model -- Part II. Automorphic Forms and Cusp Forms: -- 5. Growth conditions, automorphic forms -- 6. Poincare series -- 7. Constant term:the fundamental estimate -- 8. Finite dimensionality of the space of automorphic forms of a given type -- 9. Convolution operators on cuspidal functions -- Part III. Eisenstein Series: -- 10. Definition and convergence of Eisenstein series -- 11. Analytic continuation of the Eisenstein series -- 12. Eisenstein series and automorphic forms orthogonal to cusp forms -- Part IV. Spectral Decomposition and Representations: -- 13. Spectral decomposition of L2(G\G)m with respect to C -- 14. Generalities on representations of G -- 15. Representations of SL2(R) -- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum -- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum -- 18. Concluding remarks |
| ctrlnum | (ZDB-20-CBO)CR9780511896064 (OCoLC)890988271 (DE-599)BVBBV043942179 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511896064 |
| format | Electronic eBook |
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| id | DE-604.BV043942179 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511896064 |
| language | English |
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| publishDate | 1997 |
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| spelling | Borel, Armand Verfasser aut Automorphic forms on SL2(R) Armand Borel Automorphic forms on SL 2 (R) Cambridge Cambridge University Press 1997 1 Online-Ressource (x, 192 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 130 Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: -- 1. Prerequisites and notation -- 2. Review of SL2(R), differential operators, convolution -- 3. Action of G on X, discrete subgroups of G, fundamental domains -- 4. The unit disc model -- Part II. Automorphic Forms and Cusp Forms: -- 5. Growth conditions, automorphic forms -- 6. Poincare series -- 7. Constant term:the fundamental estimate -- 8. Finite dimensionality of the space of automorphic forms of a given type -- 9. Convolution operators on cuspidal functions -- Part III. Eisenstein Series: -- 10. Definition and convergence of Eisenstein series -- 11. Analytic continuation of the Eisenstein series -- 12. Eisenstein series and automorphic forms orthogonal to cusp forms -- Part IV. Spectral Decomposition and Representations: -- 13. Spectral decomposition of L2(G\G)m with respect to C -- 14. Generalities on representations of G -- 15. Representations of SL2(R) -- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum -- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum -- 18. Concluding remarks This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book Automorphic forms Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-58049-6 Erscheint auch als Druck-Ausgabe 978-0-521-07212-0 https://doi.org/10.1017/CBO9780511896064 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Borel, Armand Automorphic forms on SL2(R) Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane: -- 1. Prerequisites and notation -- 2. Review of SL2(R), differential operators, convolution -- 3. Action of G on X, discrete subgroups of G, fundamental domains -- 4. The unit disc model -- Part II. Automorphic Forms and Cusp Forms: -- 5. Growth conditions, automorphic forms -- 6. Poincare series -- 7. Constant term:the fundamental estimate -- 8. Finite dimensionality of the space of automorphic forms of a given type -- 9. Convolution operators on cuspidal functions -- Part III. Eisenstein Series: -- 10. Definition and convergence of Eisenstein series -- 11. Analytic continuation of the Eisenstein series -- 12. Eisenstein series and automorphic forms orthogonal to cusp forms -- Part IV. Spectral Decomposition and Representations: -- 13. Spectral decomposition of L2(G\G)m with respect to C -- 14. Generalities on representations of G -- 15. Representations of SL2(R) -- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum -- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum -- 18. Concluding remarks Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4003972-9 |
| title | Automorphic forms on SL2(R) |
| title_alt | Automorphic forms on SL 2 (R) |
| title_auth | Automorphic forms on SL2(R) |
| title_exact_search | Automorphic forms on SL2(R) |
| title_full | Automorphic forms on SL2(R) Armand Borel |
| title_fullStr | Automorphic forms on SL2(R) Armand Borel |
| title_full_unstemmed | Automorphic forms on SL2(R) Armand Borel |
| title_short | Automorphic forms on SL2(R) |
| title_sort | automorphic forms on sl2 r |
| topic | Automorphic forms Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Automorphic forms Automorphe Form |
| url | https://doi.org/10.1017/CBO9780511896064 |
| work_keys_str_mv | AT borelarmand automorphicformsonsl2r |