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• catalog abstract ""The relative quadratic case was first settled by Hecke in 1923, then recast by Weil in 1964 into the language of unitary group representations. The analytic proof of the general n-th order case is still an open problem today, going back to the end of Heckes famous treatise of 1923. The Fourier-Analytic Proof of Quadratic Reciprocity provides number theorists interested in analytic methods applied to reciprocity laws with a unique opportunity to explore the works of Hecke, Weil, and Kubota." "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 goes a step further, presenting Kubota's algebraic reformulation of the Hecke-Weil proof. Extensive commutative diagrams for comparing the Weil and Kubota architectures are also featured."--Jacket.".
• catalog contributor b11599069.
• catalog created "2000.".
• catalog date "2000".
• catalog date "2000.".
• catalog dateCopyrighted "2000.".
• catalog description ""The relative quadratic case was first settled by Hecke in 1923, then recast by Weil in 1964 into the language of unitary group representations. The analytic proof of the general n-th order case is still an open problem today, going back to the end of Heckes famous treatise of 1923. The Fourier-Analytic Proof of Quadratic Reciprocity provides number theorists interested in analytic methods applied to reciprocity laws with a unique opportunity to explore the works of Hecke, Weil, and Kubota."".
• catalog description ""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 goes a step further, presenting Kubota's algebraic reformulation of the Hecke-Weil proof. Extensive commutative diagrams for comparing the Weil and Kubota architectures are also featured."--Jacket.".
• catalog description "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.".
• catalog description "Includes bibliographical references and index.".
• catalog extent "xx, 115 p. :".
• catalog identifier "0471358304 (alk. paper)".
• catalog isPartOf "Pure and applied mathematics (John Wiley & Sons : Unnumbered)".
• catalog isPartOf "Pure and applied mathematics".
• catalog issued "2000".
• catalog issued "2000.".
• catalog language "eng".
• catalog publisher "New York : Wiley,".
• catalog subject "512/.74 21".
• catalog subject "QA241 .B47 2000".
• catalog subject "Reciprocity theorems.".
• catalog tableOfContents "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.".
• catalog title "The Fourier-analytic proof of quadratic reciprocity / Michael C. Berg.".
• catalog type "text".