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Convolution and EquidistributionSato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)$
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Nicholas M. Katz

Print publication date: 2012

Print ISBN-13: 9780691153308

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153308.001.0001

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(p.7) Chapter 1 Overview
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter provides an overview of the present analysis, which grew out of two questions, raised by Ron Evans and Zeev Rudnick respectively, in May and June of 2003. Evans and Rudnick performed numerical experiments on the sums as χ‎ varies over all multiplicative characters of k, and as χ‎ varies over all nontrivial multiplicative characters of a finite field k of odd characteristic, respectively. Both equidistribution results of Evans and Rudnick are proven.

Keywords:   number theory, exponential sums, Ron Evans, Zeeev Rudnick

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