Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / Nicholas M. Katz.

Format:

Book

Author/Creator:

Katz, Nicholas M., 1943-

Series:

Annals of mathematics studies ; no. 180.

Annals of mathematics studies ; no. 180

Language:

English

Subjects (All):

Mellin transform.

Convolutions (Mathematics).

Sequences (Mathematics).

Physical Description:

vi, 203 pages ; 24 cm.

Place of Publication:

Princeton [N.J.] : Princeton University Press, 2012.

Summary:

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty- first century as Princeton University Press publishes the major works of the new millennium.

To mark the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press web site: www.press.princeton.edu. The most recently published volumes include:

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces, Joram Lindenstrauss, David Preiss, and Jaroslav Tiser

The Ambient Metric, Charles Fefferman and C. Robin Graham

Hypoelliptic Laplacian and Orbital Integrals, Jean-Michel Bismut

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime, edited by Bas Edixhoven & Jean-Marc Couveignes

Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory, Ben Brubaker, Daniel Bump, and Solomon Friedberg

Introduction to Ramsey Spaces, Stevo Todorcevic

On the Cohomology of Certain Non-Compact Shimura Varieties, Sophie Morel

The Ergodic Theory of Lattice Subgroups, Alexander Gorodnik and Amos Nevo

Outer Billiards on Kites, Richard Evan Schwartz

Higher Topos Theory, Jacob Lurie

Classifying Spaces of Degenerating Polarized Hodge Structures, Kazuya Kato and Sampei Usui

The Structure of Affine Buildings, Richard M. Weiss

The Hypoelliptic Laplacian and Ray-Singer Metrics, Jean-Michel Bismut and Gilles Lebeau Book jacket.

Contents:

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 G_geom. and G_arith 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 G_arith 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.

Notes:

Includes bibliographical references and index.

ISBN:

9780691153308

0691153302

9780691153315

0691153310

OCLC:

748290724