Spectral decomposition and Eisenstein series: une paraphrase de l'écriture
The decomposition of the space L2(G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1995
|
| Series: | Cambridge tracts in mathematics
113 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The decomposition of the space L2(G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain subgroups of G. This book describes this proof in detail. The starting point is the theory of automorphic forms, which can also serve as a first step towards understanding the Arthur–Selberg trace formula. To make the book reasonably self-contained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudo-series, and their properties. It is thus also an introduction, suitable for graduate students, to the theory of automorphic forms, the first written using contemporary terminology. It will be welcomed by number theorists, representation theorists and all whose work involves the Langlands program |
| Physical Description: | 1 Online-Ressource (xxvii, 338 Seiten) |
| ISBN: | 9780511470905 |
| DOI: | 10.1017/CBO9780511470905 |
Staff View
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| 505 | 8 | |a I. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f) | |
| 520 | |a The decomposition of the space L2(G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain subgroups of G. This book describes this proof in detail. The starting point is the theory of automorphic forms, which can also serve as a first step towards understanding the Arthur–Selberg trace formula. To make the book reasonably self-contained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudo-series, and their properties. It is thus also an introduction, suitable for graduate students, to the theory of automorphic forms, the first written using contemporary terminology. It will be welcomed by number theorists, representation theorists and all whose work involves the Langlands program | ||
| 650 | 4 | |a Eisenstein series | |
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 4 | |a Decomposition (Mathematics) | |
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Record in the Search Index
| _version_ | 1804176883612385280 |
|---|---|
| any_adam_object | |
| author | Moeglin, Colette 1953- |
| author_GND | (DE-588)111560519 (DE-588)135928125 |
| author_facet | Moeglin, Colette 1953- |
| author_role | aut |
| author_sort | Moeglin, Colette 1953- |
| author_variant | c m cm |
| building | Verbundindex |
| bvnumber | BV043941619 |
| classification_rvk | SK 620 SK 230 |
| collection | ZDB-20-CBO |
| contents | I. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f) |
| ctrlnum | (ZDB-20-CBO)CR9780511470905 (OCoLC)849903380 (DE-599)BVBBV043941619 |
| dewey-full | 515/.243 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.243 |
| dewey-search | 515/.243 |
| dewey-sort | 3515 3243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511470905 |
| format | Electronic eBook |
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| id | DE-604.BV043941619 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511470905 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350589 |
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| physical | 1 Online-Ressource (xxvii, 338 Seiten) |
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| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Cambridge University Press |
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| spelling | Moeglin, Colette 1953- Verfasser (DE-588)111560519 aut Spectral decomposition and Eisenstein series une paraphrase de l'écriture C. Moeglin, J.-L. Waldspurger Spectral Decomposition & Eisenstein Series Cambridge Cambridge University Press 1995 1 Online-Ressource (xxvii, 338 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 113 I. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f) The decomposition of the space L2(G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain subgroups of G. This book describes this proof in detail. The starting point is the theory of automorphic forms, which can also serve as a first step towards understanding the Arthur–Selberg trace formula. To make the book reasonably self-contained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudo-series, and their properties. It is thus also an introduction, suitable for graduate students, to the theory of automorphic forms, the first written using contemporary terminology. It will be welcomed by number theorists, representation theorists and all whose work involves the Langlands program Eisenstein series Automorphic forms Spectral theory (Mathematics) Decomposition (Mathematics) Eisenstein-Reihe (DE-588)4131762-2 gnd rswk-swf Spektraldarstellung (DE-588)4182162-2 gnd rswk-swf Spektraldarstellung (DE-588)4182162-2 s Eisenstein-Reihe (DE-588)4131762-2 s DE-604 Waldspurger, Jean-Loup 1953- Sonstige (DE-588)135928125 oth Erscheint auch als Druck-Ausgabe 978-0-521-41893-5 Erscheint auch als Druck-Ausgabe 978-0-521-07035-5 https://doi.org/10.1017/CBO9780511470905 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Moeglin, Colette 1953- Spectral decomposition and Eisenstein series une paraphrase de l'écriture I. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f) Eisenstein series Automorphic forms Spectral theory (Mathematics) Decomposition (Mathematics) Eisenstein-Reihe (DE-588)4131762-2 gnd Spektraldarstellung (DE-588)4182162-2 gnd |
| subject_GND | (DE-588)4131762-2 (DE-588)4182162-2 |
| title | Spectral decomposition and Eisenstein series une paraphrase de l'écriture |
| title_alt | Spectral Decomposition & Eisenstein Series |
| title_auth | Spectral decomposition and Eisenstein series une paraphrase de l'écriture |
| title_exact_search | Spectral decomposition and Eisenstein series une paraphrase de l'écriture |
| title_full | Spectral decomposition and Eisenstein series une paraphrase de l'écriture C. Moeglin, J.-L. Waldspurger |
| title_fullStr | Spectral decomposition and Eisenstein series une paraphrase de l'écriture C. Moeglin, J.-L. Waldspurger |
| title_full_unstemmed | Spectral decomposition and Eisenstein series une paraphrase de l'écriture C. Moeglin, J.-L. Waldspurger |
| title_short | Spectral decomposition and Eisenstein series |
| title_sort | spectral decomposition and eisenstein series une paraphrase de l ecriture |
| title_sub | une paraphrase de l'écriture |
| topic | Eisenstein series Automorphic forms Spectral theory (Mathematics) Decomposition (Mathematics) Eisenstein-Reihe (DE-588)4131762-2 gnd Spektraldarstellung (DE-588)4182162-2 gnd |
| topic_facet | Eisenstein series Automorphic forms Spectral theory (Mathematics) Decomposition (Mathematics) Eisenstein-Reihe Spektraldarstellung |
| url | https://doi.org/10.1017/CBO9780511470905 |
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