Convolution and Equidistribution

Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Nonfiction, Science & Nature, Mathematics, Number Theory, Statistics
Cover of the book Convolution and Equidistribution by Nicholas M. Katz, Princeton University Press
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Author: Nicholas M. Katz ISBN: 9781400842704
Publisher: Princeton University Press Publication: January 24, 2012
Imprint: Princeton University Press Language: English
Author: Nicholas M. Katz
ISBN: 9781400842704
Publisher: Princeton University Press
Publication: January 24, 2012
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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