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

By:

Katz, Nicholas M

Material type: Text

TextSeries: Annals of mathematics studies ; no. 180.Publication details: Princeton : Princeton University Press, 2012.Description: 1 online resource (213 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781400842704
1400842700
1283379961
9781283379960

Subject(s): Genre/Form:

Additional physical formats: Print version:: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms.DDC classification:

515.723

LOC classification:

QA432 .K388 2012

Other classification:

SI 830

Online resources:

Click here to access online

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.

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.

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Item type	Home library	Collection	Call number	Materials specified	Status	Date due	Barcode
Electronic-Books	OPJGU Sonepat- Campus	E-Books EBSCO			Available

Print version record.

Includes bibliographical references and index.

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.

In English.

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