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Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms

Author
Katz, Nicholas M., 1943-
Published
Princeton : Princeton University Press, 2012.
Physical Description
1 online resource (213 pages).
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Series
Language Note
In English.
Contents
Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case. and Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography.
Summary
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 and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a.
Subject(s)
ISBN
9781400842704 (electronic bk.)
1400842700 (electronic bk.)
1283379961
9781283379960
1400842700
9780691153308 (hardcover ; alk. paper)
9780691153315 (pbk. ; alk. paper)
0691153302
0691153310
Bibliography Note
Includes bibliographical references and index.
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