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Convolution and Equidistribution
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Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Nicholas M. Katz

Abstract

This book 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 ... More

Keywords: number theory, exponential sums, finite fields, Mellin transform, algebro-geometric

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780691153308
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691153308.001.0001

Authors

Affiliations are at time of print publication.

Nicholas M. Katz, author
Princeton University

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