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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