Nicholas M Katz

(Author)

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin TransformsPaperback, 24 January 2012

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms
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Part of Series
Annals of Mathematics Studies
Part of Series
Annals of Mathematics Studies (Paperback)
Print Length
208 pages
Language
English
Publisher
Princeton University Press
Date Published
24 Jan 2012
ISBN-10
0691153310
ISBN-13
9780691153315

Description

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 probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods.

By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.

Product Details

Author:
Nicholas M Katz
Book Format:
Paperback
Country of Origin:
US
Date Published:
24 January 2012
Dimensions:
23.11 x 15.49 x 1.52 cm
ISBN-10:
0691153310
ISBN-13:
9780691153315
Language:
English
Location:
Princeton
Pages:
208
Weight:
317.51 gm

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