Katz Moments, Monodromy, and Perversity

A Diophantine Perspective
1. Auflage 2016
ISBN: 978-1-4008-2695-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 159, 488 Seiten

Reihe: Annals of Mathematics Studies

KatzNicholas M.:

Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of five previous books in this series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; and Twisted L-Functions and Monodromy.Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of five previous books in this series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; and Twisted L-Functions and Monodromy.

Autoren/Hrsg.

Katz, Nicholas M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

Introduction 1

Chapter 1: Basic results on perversity and higher moments 9

Chapter 2: How to apply the results of Chapter 2 93

Chapter 3: Additive character sums on An 111

Chapter 4: Additive character sums on more general X 161

Chapter 5: Multiplicative character sums on An 185

Chapter 6: Middle addivitve convolution 221

Appendix A6: Swan-minimal poles 281

Chapter 7: Pullbacks to curves from A1 295

Chapter 8: One variable twists on curves 321

Chapter 9: Weierstrass sheaves as inputs 327

Chapter 10: Weirstrass families 349

Chapter 11: FJTwist families and variants 371

Chapter 12: Uniformity results 407

Chapter 13: Average analytic rank and large N limits 443

References 455

Notation Index 461

Subject Index 467

Über Autor(innen)

Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of five previous books in this series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; and Twisted L-Functions and Monodromy.