PREFACE
ACKNOWLEDGMENTS
INTRODUCTION
1. Hecke's Proof of Quadratic Reciprocity
1.1 Hecke 9-functions and Their Functional Equation
1.2 Gauss(-Hecke) Sums
1.3 Relative Quadratic Reciprocity
1.4 Endnotes to Chapter 1
2.Two Equivalent Forms of Quadratic Reciprocity
3.The Stone-Von Neumann Theorem
3.1 The Finite Case:A Paradigm
3.2 The Locally Compact Abelian Case: Some Remarks
3.3 The Form of the Stone-Von Neumann Theorem Used
in 8 4
4.Weil's"Acta"Paper
4.1 Heisenberg Groups
4.2 A Heisenberg Group and A Group of Unitary
Operators
4.3 The Kernel of T
4.4 Second-Degree Characters
4.5 The Splitting of T on a Distinguished Subgroup of
B(G)
4.6 Vector Spaces Over Local Fields
4.7 Quaternions Over a Local Field
4.8 Hilbert Reciprocity
4.9 The Stone-Von Neumann Theorem Revisited
4.10 The Double Cover of the Symplectic Group
4.11 Endnotes to Chapter 4
5.Kubota and Cohomology
5.1 Weil Revisited
5.2 Kubota's Cocycle
5.3 The Splitting of a Over SL(2,k)
5.4 2-Hilbert Reciprocity Once Again
6.The Algebraic Agreement Between the Formalisms of Weil
and Kubota
6.1 The Gruesome Diagram
6.2 The Even More Gruesome Diagram
7.Hecke's Challenge: General Reciprocity and Fourier
Analysis on the March
BIBLIOGRAPHY
INDEX
编辑手记
展开