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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) Book

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180), Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results , Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
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  • Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)
  • Written by author Nicholas M. Katz
  • Published by Princeton University Press, 2/26/2012
  • Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results
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Book Categories

Authors

Introduction 1

Chapter 1 Overview 7

Chapter 2 Convolution of Perverse Sheaves 19

Chapter 3 Fibre Functors 21

Chapter 4 The Situation over a Finite Field 25

Chapter 5 Frobenius Conjugacy Classes 31

Chapter 6 Group-Theoretic Facts about Ggeom and Garith 33

Chapter 7 The Main Theorem 39

Chapter 8 Isogenies, Connectedness, and Lie-Irreducibility 45

Chapter 9 Autodualities and Signs 49

Chapter 10 A First Construction of Autodual Objects 53

Chapter 11 A Second Construction of Autodual Objects 55

Chapter 12 The Previous Construction in the Nonsplit Case 61

Chapter 13 Results of Goursat-Kolchin-Ribet Type 63

Chapter 14 The Case of SL(2); the Examples of Evans and Rudnick 67

Chapter 15 Further SL(2) Examples, Based on the Legendre Family 73

Chapter 16 Frobenius Tori and Weights; Getting Elements of Garith 77

Chapter 17 GL(n) Examples 81

Chapter 18 Symplectic Examples 89

Chapter 19 Orthogonal Examples, Especially SO(n) Examples 103

Chapter 20 GL(n) × GL(n) × ... × GL(n) Examples 113

Chapter 21 SL(n) Examples, for n an Odd Prime 125

Chapter 22 SL(n) Examples with Slightly Composite n 135

Chapter 23 Other SL(n) Examples 141

Chapter 24 An O(2n) Example 145

Chapter 25 G2 Examples: the Overall Strategy 147

Chapter 26 G2 Examples: Construction in Characteristic Two 155

Chapter 27 G2 Examples: Construction in Odd Characteristic 163

Chapter 28 The Situation over Z: Results 173

Chapter 29 The Situation over Z: Questions 181

Chapter 30 Appendix: Deligne's Fibre Functor 187

Bibliography 193


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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180), <i>Convolution and Equidistribution</i> explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results , Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180), <i>Convolution and Equidistribution</i> explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results , Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180), <i>Convolution and Equidistribution</i> explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results , Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

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