The Fourier analytic proof of quadratic reciprocity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Series: | Pure and applied mathematics
A Wiley interscience publication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 115 S. |
| ISBN: | 0471358304 |
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MARC
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| 245 | 1 | 0 | |a The Fourier analytic proof of quadratic reciprocity |c Michael C. Berg |
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Record in the Search Index
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| adam_text | Contents
PREFACE vii
ACKNOWLEDGMENTS xi
INTRODUCTION xiii
1. Hecke s Proof of Quadratic Reciprocity 1
1.1 Hecke ^ functions and Their Functional Equation
/ 3
1.2 Gauss ( Hecke) Sums / 5
1.3 Relative Quadratic Reciprocity / 11
1.4 Endnotes to Chapter 1/14
2. Two Equivalent Forms of Quadratic Reciprocity 16
3. The Stone Von Neumann Theorem 20
3.1 The Finite Case: A Paradigm / 21
3.2 The Locally Compact Abelian Case: Some Remarks
/ 24
3.3 The Form of the Stone Von Neumann Theorem Used
in § 4.1 / 25
v
VI CONTENTS
4. Weil s Acta Paper 26
4.1 Heisenberg Groups / 28
4.2 A Heisenberg Group and A Group of Unitary
Operators / 32
4.3 The Kernel of tt / 35
4.4 Second Degree Characters / 44
4.5 The Splitting of 77 on a Distinguished Subgroup of
B(G) / 52
4.6 Vector Spaces Over Local Fields / 57
4.7 Quaternions Over a Local Field / 63
4.8 Hilbert Reciprocity / 70
4.9 The Stone Von Neumann Theorem Revisited / 73
4.10 The Double Cover of the Symplectic Group / 77
4.11 Endnotes to Chapter 4/79
5. Kubota and Cohomology 82
5.1 Weil Revisited / 84
5.2 Kubota s Cocycle / 86
5.3 The Splitting of aA Over SL(2, k) / 92
5.4 2 Hilbert Reciprocity Once Again / 96
6. The Algebraic Agreement Between the Formalisms of Weil
and Kubota 98
6.1 The Gruesome Diagram / 99
6.2 The Even More Gruesome Diagram / 102
7. Hecke s Challenge: General Reciprocity and Fourier
Analysis on the March 103
BIBLIOGRAPHY 109
INDEX 113
|
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| id | DE-604.BV013405198 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:45:18Z |
| institution | BVB |
| isbn | 0471358304 |
| language | English |
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| physical | XX, 115 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics A Wiley interscience publication |
| spelling | Berg, Michael C. Verfasser aut The Fourier analytic proof of quadratic reciprocity Michael C. Berg New York [u.a.] Wiley 2000 XX, 115 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics A Wiley interscience publication Quadratisches Reziprozitätsgesetz (DE-588)4176566-7 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Quadratisches Reziprozitätsgesetz (DE-588)4176566-7 s Beweis (DE-588)4132532-1 s Harmonische Analyse (DE-588)4023453-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009146620&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berg, Michael C. The Fourier analytic proof of quadratic reciprocity Quadratisches Reziprozitätsgesetz (DE-588)4176566-7 gnd Beweis (DE-588)4132532-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4176566-7 (DE-588)4132532-1 (DE-588)4023453-8 |
| title | The Fourier analytic proof of quadratic reciprocity |
| title_auth | The Fourier analytic proof of quadratic reciprocity |
| title_exact_search | The Fourier analytic proof of quadratic reciprocity |
| title_full | The Fourier analytic proof of quadratic reciprocity Michael C. Berg |
| title_fullStr | The Fourier analytic proof of quadratic reciprocity Michael C. Berg |
| title_full_unstemmed | The Fourier analytic proof of quadratic reciprocity Michael C. Berg |
| title_short | The Fourier analytic proof of quadratic reciprocity |
| title_sort | the fourier analytic proof of quadratic reciprocity |
| topic | Quadratisches Reziprozitätsgesetz (DE-588)4176566-7 gnd Beweis (DE-588)4132532-1 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Quadratisches Reziprozitätsgesetz Beweis Harmonische Analyse |
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