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Arithmetic geometry and number theory [[electronic resource] /] / editors, Lin Weng, Iku Nakamura
| Arithmetic geometry and number theory [[electronic resource] /] / editors, Lin Weng, Iku Nakamura |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 512.7 |
| Altri autori (Persone) |
WengLin <1964->
NakamuraIku |
| Collana | Series on number theory and its applications |
| Soggetto topico |
Number theory
Algebra |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-92483-0
9786611924836 981-277-353-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; On Local y-Factors; 1 Introduction; 2 Basic Properties of Local y-Factors; 2.1 Multiplicativity; 2.2 Stability; 2.3 Remarks; 3 Local Converse Theorems; 3.1 The case of GLn(F); 3.2 A conjectural LCT; 3.3 The case of SO2n+1(F); 4 Poles of Local y-Factors; 4.1 The case of G = SO2n+1; 4.2 Other classical groups; Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces; 1 WP Metrics and TZ Metrics; 2 Line Bundles over Moduli Spaces; 3 Fundamental Relations on MgN' Algebraic Story; 4 Fundamental Relation on MgN- Arithmetic Story; 5 Deligne Tuple in General
6 Degeneration of TZ Metrics: Analytic StoryReferences; Vector Bundles on Curves over Cp; 1 Introduction; 2 Complex Vector Bundles; 3 Fundamental Groups of p-Adic Curves; 4 Finite Vector Bundles; 5 A Bigger Category of Vector Bundles; 6 Parallel Transport on Bundles in Bxcp; 7 Working Outside a Divisor on Xcp; 8 Properties of Parallel Transport; 9 Semistable Bundles; 10 A Simpler Description of Bxcp D; 11 Strongly Semistable Reduction; 12 How Big are our Categories of Bundles?; 13 Representations of the Fundamental Group; 14 Mumford Curves; References Absolute CM-periods -- Complex and p-Adic1 Introduction; 2 Notation; 2.1 Complex Theory; 2.2 p-Adic Theory; References; Special Zeta Values in Positive Characteristic; 1 Introduction; 2 Carlitz Theory; 3 Anderson-Thakur Theory; 4 t-Motives; 5 Algebraic Independence of the Special Zeta Values; References; Automorphic Forms & Eisenstein Series and Spectral Decompositions; Day One: Basics of Automorphic Forms; 1 Basic Decompositions; 1.1 Langlands Decomposition; 1.2 Reduction Theory: Siegel Sets; 1.3 Moderate Growth and Rapidly Decreasing; 1.4 Automorphic Forms; 2 Structural Results 2.1 Moderate Growth and Rapid Decreasing2.2 Semi-Simpleness; 2.3 3-Finiteness; 2.4 Philosophy of Cusp Forms; 2.5 L2-Automorphic Forms; Day Two: Eisenstein Series; 3 Definition; 3.1 Equivalence Classes of Automorphic Representations; 3.2 Eisenstein Series and Intertwining Operators; 3.3 Convergence; 4 Constant Terms of Eisenstein Series; 5 Fundamental Properties of Eisenstein Series; Day Three: Pseudo-Eisenstein Series; 6 Paley-Wiener Functions; 6.1 Paley-Wiener Functions; 6.2 Fourier Transforms; 6.3 Paley-Wiener on p; 7 Pseudo-Eisenstein Series; 8 First Decomposition of L2(G(F)\G(A))\ 8.1 Inner Product Formula for P-ESes8.2 Decomposition of L2-Spaces According to Cuspidal Data; 8.3 Constant Terms of P-SEes; 9 Decomposition of Automorphic Forms According to Cuspidal Data; 9.1 Main Result; 9.2 Langlands Operators; 9.3 Key Bridge; Day Four: Spectrum Decomposition: Residual Process; 10 Why Residue?; 10.1 Pseudo-Eisenstein Series and Residual Process; 10.2 What do we have?; 10.3 Difficulties; 11 Main Results; 11.1 Functional Analysis; 11.2 Main Theorem: Rough Version; 11.3 Main Theorem: Refined Version; 11.4 How to Prove? Day Five: Eisenstein Systems and Spectral Decomposition (II) |
| Record Nr. | UNINA-9910453225203321 |
| Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Arithmetic geometry and number theory [[electronic resource] /] / editors, Lin Weng, Iku Nakamura
| Arithmetic geometry and number theory [[electronic resource] /] / editors, Lin Weng, Iku Nakamura |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 512.7 |
| Altri autori (Persone) |
WengLin <1964->
NakamuraIku |
| Collana | Series on number theory and its applications |
| Soggetto topico |
Number theory
Algebra |
| ISBN |
1-281-92483-0
9786611924836 981-277-353-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; On Local y-Factors; 1 Introduction; 2 Basic Properties of Local y-Factors; 2.1 Multiplicativity; 2.2 Stability; 2.3 Remarks; 3 Local Converse Theorems; 3.1 The case of GLn(F); 3.2 A conjectural LCT; 3.3 The case of SO2n+1(F); 4 Poles of Local y-Factors; 4.1 The case of G = SO2n+1; 4.2 Other classical groups; Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces; 1 WP Metrics and TZ Metrics; 2 Line Bundles over Moduli Spaces; 3 Fundamental Relations on MgN' Algebraic Story; 4 Fundamental Relation on MgN- Arithmetic Story; 5 Deligne Tuple in General
6 Degeneration of TZ Metrics: Analytic StoryReferences; Vector Bundles on Curves over Cp; 1 Introduction; 2 Complex Vector Bundles; 3 Fundamental Groups of p-Adic Curves; 4 Finite Vector Bundles; 5 A Bigger Category of Vector Bundles; 6 Parallel Transport on Bundles in Bxcp; 7 Working Outside a Divisor on Xcp; 8 Properties of Parallel Transport; 9 Semistable Bundles; 10 A Simpler Description of Bxcp D; 11 Strongly Semistable Reduction; 12 How Big are our Categories of Bundles?; 13 Representations of the Fundamental Group; 14 Mumford Curves; References Absolute CM-periods -- Complex and p-Adic1 Introduction; 2 Notation; 2.1 Complex Theory; 2.2 p-Adic Theory; References; Special Zeta Values in Positive Characteristic; 1 Introduction; 2 Carlitz Theory; 3 Anderson-Thakur Theory; 4 t-Motives; 5 Algebraic Independence of the Special Zeta Values; References; Automorphic Forms & Eisenstein Series and Spectral Decompositions; Day One: Basics of Automorphic Forms; 1 Basic Decompositions; 1.1 Langlands Decomposition; 1.2 Reduction Theory: Siegel Sets; 1.3 Moderate Growth and Rapidly Decreasing; 1.4 Automorphic Forms; 2 Structural Results 2.1 Moderate Growth and Rapid Decreasing2.2 Semi-Simpleness; 2.3 3-Finiteness; 2.4 Philosophy of Cusp Forms; 2.5 L2-Automorphic Forms; Day Two: Eisenstein Series; 3 Definition; 3.1 Equivalence Classes of Automorphic Representations; 3.2 Eisenstein Series and Intertwining Operators; 3.3 Convergence; 4 Constant Terms of Eisenstein Series; 5 Fundamental Properties of Eisenstein Series; Day Three: Pseudo-Eisenstein Series; 6 Paley-Wiener Functions; 6.1 Paley-Wiener Functions; 6.2 Fourier Transforms; 6.3 Paley-Wiener on p; 7 Pseudo-Eisenstein Series; 8 First Decomposition of L2(G(F)\G(A))\ 8.1 Inner Product Formula for P-ESes8.2 Decomposition of L2-Spaces According to Cuspidal Data; 8.3 Constant Terms of P-SEes; 9 Decomposition of Automorphic Forms According to Cuspidal Data; 9.1 Main Result; 9.2 Langlands Operators; 9.3 Key Bridge; Day Four: Spectrum Decomposition: Residual Process; 10 Why Residue?; 10.1 Pseudo-Eisenstein Series and Residual Process; 10.2 What do we have?; 10.3 Difficulties; 11 Main Results; 11.1 Functional Analysis; 11.2 Main Theorem: Rough Version; 11.3 Main Theorem: Refined Version; 11.4 How to Prove? Day Five: Eisenstein Systems and Spectral Decomposition (II) |
| Record Nr. | UNINA-9910782327503321 |
| Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Arithmetic geometry and number theory / / editors, Lin Weng, Iku Nakamura
| Arithmetic geometry and number theory / / editors, Lin Weng, Iku Nakamura |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (411 p.) |
| Disciplina | 512.7 |
| Altri autori (Persone) |
WengLin <1964->
NakamuraIku |
| Collana | Series on number theory and its applications |
| Soggetto topico |
Number theory
Algebra |
| ISBN |
1-281-92483-0
9786611924836 981-277-353-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Foreword; Preface; Contents; On Local y-Factors; 1 Introduction; 2 Basic Properties of Local y-Factors; 2.1 Multiplicativity; 2.2 Stability; 2.3 Remarks; 3 Local Converse Theorems; 3.1 The case of GLn(F); 3.2 A conjectural LCT; 3.3 The case of SO2n+1(F); 4 Poles of Local y-Factors; 4.1 The case of G = SO2n+1; 4.2 Other classical groups; Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces; 1 WP Metrics and TZ Metrics; 2 Line Bundles over Moduli Spaces; 3 Fundamental Relations on MgN' Algebraic Story; 4 Fundamental Relation on MgN- Arithmetic Story; 5 Deligne Tuple in General
6 Degeneration of TZ Metrics: Analytic StoryReferences; Vector Bundles on Curves over Cp; 1 Introduction; 2 Complex Vector Bundles; 3 Fundamental Groups of p-Adic Curves; 4 Finite Vector Bundles; 5 A Bigger Category of Vector Bundles; 6 Parallel Transport on Bundles in Bxcp; 7 Working Outside a Divisor on Xcp; 8 Properties of Parallel Transport; 9 Semistable Bundles; 10 A Simpler Description of Bxcp D; 11 Strongly Semistable Reduction; 12 How Big are our Categories of Bundles?; 13 Representations of the Fundamental Group; 14 Mumford Curves; References Absolute CM-periods -- Complex and p-Adic1 Introduction; 2 Notation; 2.1 Complex Theory; 2.2 p-Adic Theory; References; Special Zeta Values in Positive Characteristic; 1 Introduction; 2 Carlitz Theory; 3 Anderson-Thakur Theory; 4 t-Motives; 5 Algebraic Independence of the Special Zeta Values; References; Automorphic Forms & Eisenstein Series and Spectral Decompositions; Day One: Basics of Automorphic Forms; 1 Basic Decompositions; 1.1 Langlands Decomposition; 1.2 Reduction Theory: Siegel Sets; 1.3 Moderate Growth and Rapidly Decreasing; 1.4 Automorphic Forms; 2 Structural Results 2.1 Moderate Growth and Rapid Decreasing2.2 Semi-Simpleness; 2.3 3-Finiteness; 2.4 Philosophy of Cusp Forms; 2.5 L2-Automorphic Forms; Day Two: Eisenstein Series; 3 Definition; 3.1 Equivalence Classes of Automorphic Representations; 3.2 Eisenstein Series and Intertwining Operators; 3.3 Convergence; 4 Constant Terms of Eisenstein Series; 5 Fundamental Properties of Eisenstein Series; Day Three: Pseudo-Eisenstein Series; 6 Paley-Wiener Functions; 6.1 Paley-Wiener Functions; 6.2 Fourier Transforms; 6.3 Paley-Wiener on p; 7 Pseudo-Eisenstein Series; 8 First Decomposition of L2(G(F)\G(A))\ 8.1 Inner Product Formula for P-ESes8.2 Decomposition of L2-Spaces According to Cuspidal Data; 8.3 Constant Terms of P-SEes; 9 Decomposition of Automorphic Forms According to Cuspidal Data; 9.1 Main Result; 9.2 Langlands Operators; 9.3 Key Bridge; Day Four: Spectrum Decomposition: Residual Process; 10 Why Residue?; 10.1 Pseudo-Eisenstein Series and Residual Process; 10.2 What do we have?; 10.3 Difficulties; 11 Main Results; 11.1 Functional Analysis; 11.2 Main Theorem: Rough Version; 11.3 Main Theorem: Refined Version; 11.4 How to Prove? Day Five: Eisenstein Systems and Spectral Decomposition (II) |
| Record Nr. | UNINA-9910806985203321 |
| Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||