Convolution and Equidistribution (eBook, 2012) [WorldCat.org]
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Convolution and Equidistribution

Author: Nicholas Katz; Safari, an O'Reilly Media Company.
Publisher: Princeton University Press, 2012.
Edition/Format:   eBook : Document : English : 1st edition
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  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Nicholas Katz; Safari, an O'Reilly Media Company.
OCLC Number: 1105790355
Description: 1 online resource (208 pages)
Responsibility: Katz, Nicholas.

Abstract:

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.

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