Fourier analysis on number fields:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg ; Barcelona ; Budapest u.a.
Springer
1999
|
| Schriftenreihe: | Graduate texts in mathematics
186 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 339 - 343 Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXI, 350 S. |
| ISBN: | 0387984364 9780387984360 9781475730876 |
Internformat
MARC
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| 100 | 1 | |a Ramakrishnan, Dinakar |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fourier analysis on number fields |c Dinakar Ramakrishnan ; Robert J. Valenza |
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Budapest u.a. |b Springer |c 1999 | |
| 300 | |a XXI, 350 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 186 | |
| 500 | |a Literaturverz. S. 339 - 343 | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Topologische Gruppe - Harmonische Analyse | |
| 650 | 4 | |a Zahlentheorie | |
| 650 | 4 | |a Fourier analysis | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Topological groups | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologische Gruppe |0 (DE-588)4135793-0 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Valenza, Robert J. |e Verfasser |4 aut | |
| 830 | 0 | |a Graduate texts in mathematics |v 186 |w (DE-604)BV000000067 |9 186 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008428537 | |
Datensatz im Suchindex
| _version_ | 1811176903837483008 |
|---|---|
| adam_text |
Contents
Preface vii
Index of Notation xv
1 Topological Groups
1.1 Basic Notions 1
1.2 Haar Measure 9
1.3 Profinite Groups 19
1.4 Pro p Groups 36
Exercises 42
2 Some Representation Theory
2.1 Representations of Locally Compact Groups 46
2.2 Banach Algebras and the Gelfand Transform 50
2.3 The Spectral Theorems 60
2.4 Unitary Representations 73
Exercises 78
3 Duality for Locally Compact Abelian Groups
3.1 The Pontryagin Dual 86
3.2 Functions of Positive Type 91
3.3 The Fourier Inversion Formula 102
3.4 Pontryagin Duality 118
Exercises 125
xii Contents
4 The Structure of Arithmetic Fields
4.1 The Module of an Automorphism 132
4.2 The Classification of Locally Compact Fields 140
4.3 Extensions of Local Fields 150
4.4 Places and Completions of Global Fields 154
4.5 Ramification and Bases 165
Exercises 174
5 Adeles, Ideles, and the Class Groups
5.1 Restricted Direct Products, Characters, and Measures 180
5.2 Adeles, Ideles, and the Approximation Theorem 189
5.3 The Geometry of A^K 191
5.4 The Class Groups 196
Exercises 208
6 A Quick Tour of Class Field Theory
6.1 Frobenius Elements 214
6.2 The Tchebotarev Density Theorem 219
6.3 The Transfer Map 220
6.4 Artin's Reciprocity Law 222
6.5 Abelian Extensions of Q and Qp 226
Exercises 238
7 Tate' s Thesis and Applications
7.1 Local ^ Functions 243
7.2 The Riemann Roch Theorem 259
7.3 The Global Functional Equation 269
7.4 Hecke L Functions 276
7.5 The Volume of C\ and the Regulator 281
7.6 Dirichlet's Class Number Formula 286
7.7 NonvanishingontheLineRe(s)=l 289
7.8 Comparison of Hecke Z, Functions 295
Exercises 297
Contents xiii
Appendices
Appendix A: NormedLinear Spaces
A.1 Finite Dimensional Normed Linear Spaces 315
A.2 The Weak Topology 317
A.3 The Weak Star Topology 319
A.4 A Review of Z,' Spaces and Duality 323
Appendix B: DedekindDomains
B.I Basic Properties 326
B.2 Extensions of Dedekind Domains 334
References 339
Index 345 |
| any_adam_object | 1 |
| author | Ramakrishnan, Dinakar Valenza, Robert J. |
| author_facet | Ramakrishnan, Dinakar Valenza, Robert J. |
| author_role | aut aut |
| author_sort | Ramakrishnan, Dinakar |
| author_variant | d r dr r j v rj rjv |
| building | Verbundindex |
| bvnumber | BV012421561 |
| callnumber-first | Q - Science |
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| classification_tum | MAT 220f MAT 430f MAT 122f |
| ctrlnum | (OCoLC)245734270 (DE-599)BVBBV012421561 |
| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-09-25T14:01:35Z |
| institution | BVB |
| isbn | 0387984364 9780387984360 9781475730876 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008428537 |
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| physical | XXI, 350 S. |
| publishDate | 1999 |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Ramakrishnan, Dinakar Verfasser aut Fourier analysis on number fields Dinakar Ramakrishnan ; Robert J. Valenza New York ; Berlin ; Heidelberg ; Barcelona ; Budapest u.a. Springer 1999 XXI, 350 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 186 Literaturverz. S. 339 - 343 Hier auch später erschienene, unveränderte Nachdrucke Topologische Gruppe - Harmonische Analyse Zahlentheorie Fourier analysis Number theory Topological groups Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 s Harmonische Analyse (DE-588)4023453-8 s DE-604 Zahlentheorie (DE-588)4067277-3 s Valenza, Robert J. Verfasser aut Graduate texts in mathematics 186 (DE-604)BV000000067 186 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramakrishnan, Dinakar Valenza, Robert J. Fourier analysis on number fields Graduate texts in mathematics Topologische Gruppe - Harmonische Analyse Zahlentheorie Fourier analysis Number theory Topological groups Harmonische Analyse (DE-588)4023453-8 gnd Zahlentheorie (DE-588)4067277-3 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4067277-3 (DE-588)4135793-0 |
| title | Fourier analysis on number fields |
| title_auth | Fourier analysis on number fields |
| title_exact_search | Fourier analysis on number fields |
| title_full | Fourier analysis on number fields Dinakar Ramakrishnan ; Robert J. Valenza |
| title_fullStr | Fourier analysis on number fields Dinakar Ramakrishnan ; Robert J. Valenza |
| title_full_unstemmed | Fourier analysis on number fields Dinakar Ramakrishnan ; Robert J. Valenza |
| title_short | Fourier analysis on number fields |
| title_sort | fourier analysis on number fields |
| topic | Topologische Gruppe - Harmonische Analyse Zahlentheorie Fourier analysis Number theory Topological groups Harmonische Analyse (DE-588)4023453-8 gnd Zahlentheorie (DE-588)4067277-3 gnd Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Topologische Gruppe - Harmonische Analyse Zahlentheorie Fourier analysis Number theory Topological groups Harmonische Analyse Topologische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008428537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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