Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116

by Nicholas M. Katz

Overview

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.

Product Details

ISBN-13:	9781400882120
Publisher:	Princeton University Press
Publication date:	03/02/2016
Series:	Annals of Mathematics Studies , #116
Sold by:	Barnes & Noble
Format:	eBook
Pages:	256
File size:	10 MB

Table of Contents

• Frontmatter, pg. i
• Contents, pg. v
• Introduction, pg. 1
• CHAPTER 1. Breaks and Swan Conductors, pg. 12
• CHAPTER 2. Curves and Their Cohomology, pg. 26
• CHAPTER 3. Equidistribution in Equal Characteristic, pg. 36
• CHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves, pg. 46
• CHAPTER 5. Convolution of Sheaves on Gm, pg. 62
• CHAPTER 6. Local Convolution, pg. 87
• CHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study, pg. 96
• CHAPTER 8. Complements on Convolution, pg. 120
• CHAPTER 9. Equidistribution in (S1)r of r-tuples of Angles of Gauss Sums, pg. 155
• CHAPTER 10. Local Monodromy at ∞ of Kloosterman Sheaves, pg. 168
• CHAPTER 11. Global Monodromy of Kloosterman Sheaves, pg. 176
• CHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d’après O. Gabber), pg. 210
• CHAPTER 13. Equidistribution of “Angles” of Kloosterman Sums, pg. 234
• References, pg. 243