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The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg
| The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg |
| Autore | Berg Michael C. <1955-> |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 2000 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 512.74 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts |
| Soggetto topico | Reciprocity theorems |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-03294-2
1-118-03119-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910141242203321 |
Berg Michael C. <1955->
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg
| The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg |
| Autore | Berg Michael C. <1955-> |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 2000 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 512.74 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts |
| Soggetto topico | Reciprocity theorems |
| ISBN |
1-118-03294-2
1-118-03119-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNISA-996205526203316 |
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Berg Michael C. <1955->
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg
| The fourier-analytic proof of quadratic reciprocity / / Michael C. Berg |
| Autore | Berg Michael C. <1955-> |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 2000 |
| Descrizione fisica | 1 online resource (142 p.) |
| Disciplina | 512.74 |
| Collana | Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts |
| Soggetto topico | Reciprocity theorems |
| ISBN |
1-118-03294-2
1-118-03119-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910829889303321 |
|
Berg Michael C. <1955->
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 2000 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||