The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg

• Autore: Berg Michael C. <1955->
• Pubblicazione: New York, New York : , : John Wiley & Sons, Inc., , 2000; ©2000
• Descrizione fisica: 1 online resource (142 p.)
• Disciplina: 512.74
• Soggetto topico: Reciprocity theorems
• Note generali: "A Wiley-Interscience Publication."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: The Fourier-Analytic Proof of Quadratic Reciprocity; Contents; PREFACE; ACKNOWLEDGMENTS; INTRODUCTION; 1. Hecke's Proof of Quadratic Reciprocity; 1.1 Hecke υ-functions and Their Functional Equation; 1.2 Gauss (-Hecke) Sums; 1.3 Relative Quadratic Reciprocity; 1.4 Endnotes to Chapter; 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 4.1; 4. Weil's ""Acta"" Paper; 4.1 Heisenberg Groups ; 4.2 A Heisenberg Group and A Group of Unitary Operators4.3 The Kernel of π; 4.4 Second-Degree Characters; 4.5 The Splitting of π 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; 5. Kubota and Cohomology; 5.1 Weil Revisited; 5.2 Kubota's Cocycle; 5.3 The Splitting of αA 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 Diagram6.2 The Even More Gruesome Diagram; 7. Hecke's Challenge: General Reciprocity and Fourier Analysis on the March; BIBLIOGRAPHY; INDEX
• Sommario/riassunto: A unique synthesis of the three existing Fourier-analytic treatments of quadratic reciprocity.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 Hecke's 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.<br
• Titolo autorizzato: Fourier-analytic proof of quadratic reciprocity
• ISBN: 1-118-03294-2; 1-118-03119-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910829889303321
• Lo trovi qui: Univ. Federico II
• Serie: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts