The Fourier-analytic proof of quadratic reciprocity /
"This work brings together for the first time in a single volume the three existing formulations of the Fourier-analytic proof of quadratic reciprocity. It shows how Weil's ground-breaking representation-theoretic treatment is in fact equivalent to Hecke's classical approach, then goe...
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| Format: | eBook |
| Language: | English |
| Published: |
New York :
Wiley,
©2000.
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| Series: | Pure and applied mathematics (John Wiley & Sons : Unnumbered)
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- 1. Hecke's Proof of Quadratic Reciprocity 1
- 1.1 Hecke [curly or open theta]-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. Stone-Von Neumann Theorem 20
- 3.1 Finite Case: A Paradigm 21
- 3.2 Locally Compact Abelian Case: Some Remarks 24
- 3.3 Form of the Stone-Von Neumann Theorem Used in [section] 4.1 25
- 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 Kernel of [pi] 35
- 4.4 Second-Degree Characters 44
- 4.5 Splitting of [pi] 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 Stone-Von Neumann Theorem Revisited 73
- 4.10 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 Splitting of [alpha subscript A] Over SL(2, k) 92
- 5.4 2-Hilbert Reciprocity Once Again 96
- 6. Algebraic Agreement Between the Formalisms of Weil and Kubota 98
- 6.1 Gruesome Diagram 99
- 6.2 Even More Gruesome Diagram 102
- 7. Hecke's Challenge: General Reciprocity and Fourier Analysis on the March 103.