Arithmetic and analytic theories of quadratic forms and Clifford groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2004]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 109 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 275 Seiten |
| ISBN: | 0821835734 9780821835739 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804132786397773824 |
|---|---|
| adam_text | TABLE OF CONTENTS
Preface vii
Notation and Terminology ix
Introduction 1
Chapter I. Algebraic theory of quadratic forms, Clifford
algebras, and spin groups 9
1. Quadratic forms and associative algebras 9
2. Clifford algebras 15
3. Clifford groups and spin groups 20
4. Parabolic subgroups 28
Chapter II. Quadratic forms, Clifford algebras, and spin
groups over a local or global field 37
5. Orders and ideals in an algebra 37
6. Quadratic forms over a local field 45
7. Lower dimensional cases and the Hasse principle 52
8. Part I. Clifford groups over a local field 62
8. Part II. Formal Hecke algebras and formal Euler factors 72
9. Orthogonal, Clifford, and spin groups over a global field 80
Chapter III. Quadratic Diophantine equations 93
10. Quadratic Diophantine equations over a local field 93
11. Quadratic Diophantine equations over a global field 101
12. The class number of an orthogonal group and sums of
squares 113
13. Nonscalar quadratic Diophantine equations: Connection
with the mass formula: A historical perspective 126
Chapter IV. Groups and symmetric spaces over R 139
14. Clifford and spin groups over R; The case of signature
(1, m) 139
15. The case of signature (2, m) 146
16. Orthogonal groups over R and symmetric spaces 154
Chapter V. Euler products and Eisenstein series on or¬
thogonal groups 163
17. Automorphic forms and Euler products on an orthogonal
group 163
V
vi
18. Eisenstein series on O^ 173
19. Eisenstein series on Ov 181
20. Arithmetic description of the pullback of an Eisenstein
series 187
21. Analytic continuation of Euler products and Eisenstein
series 196
Chapter VI. Euler products and Eisenstein series on
Clifford groups 205
22. Euler products on G+{V) 205
23. Eisenstein series on G{H, 2~1r)) 212
24. Eisenstein series of general types on a Clifford group 218
25. Euler products for holomorphic forms on a Clifford group 226
26. Proof of the last main theorem 234
Appendix 243
Al. Differential operators on a semisimple Lie group 243
A2. Eigenvalues of integral operators 250
A3. Structure of Clifford algebras over R 261
A4. An embedding of G1 (V) into a symplectic group 265
A5. Spin representations and Lie algebras 268
References 272
Frequently used symbols 274
Index 275
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:58:21Z |
| institution | BVB |
| isbn | 0821835734 9780821835739 |
| language | English |
| lccn | 2003063826 |
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| physical | ix, 275 Seiten |
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| spelling | Shimura, Goro 1930-2019 Verfasser (DE-588)12425067X aut Arithmetic and analytic theories of quadratic forms and Clifford groups Goro Shimura Providence, Rhode Island American Mathematical Society [2004] © 2004 ix, 275 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 109 Formas quadráticas larpcal Formes quadratiques Groupes linéaires algébriques Nombres, Théorie des Teoria dos números larpcal Forms, Quadratic Linear algebraic groups Number theory Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Quadratische Form (DE-588)4128297-8 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Quadratische Form (DE-588)4128297-8 s Lineare algebraische Gruppe (DE-588)4295326-1 s Zahlentheorie (DE-588)4067277-3 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1336-1 Mathematical surveys and monographs Volume 109 (DE-604)BV000018014 109 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012818637&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shimura, Goro 1930-2019 Arithmetic and analytic theories of quadratic forms and Clifford groups Mathematical surveys and monographs Formas quadráticas larpcal Formes quadratiques Groupes linéaires algébriques Nombres, Théorie des Teoria dos números larpcal Forms, Quadratic Linear algebraic groups Number theory Lineare algebraische Gruppe (DE-588)4295326-1 gnd Quadratische Form (DE-588)4128297-8 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4295326-1 (DE-588)4128297-8 (DE-588)4067277-3 |
| title | Arithmetic and analytic theories of quadratic forms and Clifford groups |
| title_auth | Arithmetic and analytic theories of quadratic forms and Clifford groups |
| title_exact_search | Arithmetic and analytic theories of quadratic forms and Clifford groups |
| title_full | Arithmetic and analytic theories of quadratic forms and Clifford groups Goro Shimura |
| title_fullStr | Arithmetic and analytic theories of quadratic forms and Clifford groups Goro Shimura |
| title_full_unstemmed | Arithmetic and analytic theories of quadratic forms and Clifford groups Goro Shimura |
| title_short | Arithmetic and analytic theories of quadratic forms and Clifford groups |
| title_sort | arithmetic and analytic theories of quadratic forms and clifford groups |
| topic | Formas quadráticas larpcal Formes quadratiques Groupes linéaires algébriques Nombres, Théorie des Teoria dos números larpcal Forms, Quadratic Linear algebraic groups Number theory Lineare algebraische Gruppe (DE-588)4295326-1 gnd Quadratische Form (DE-588)4128297-8 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Formas quadráticas Formes quadratiques Groupes linéaires algébriques Nombres, Théorie des Teoria dos números Forms, Quadratic Linear algebraic groups Number theory Lineare algebraische Gruppe Quadratische Form Zahlentheorie |
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