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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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An O(2n) Example

An O(2n) Example

(p.145) Chapter 24 An O(2n) Example
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter works over a finite field k of odd characteristic. Fix an even integer 2n ≤ 4 and a monic polynomial f(x) ɛ k[x] of degree 2n, f(x)=∑i=02nAixi, A2n=1. The following three assumptions are made about f: (1) f has 2n distinct roots in k¯, and A₀ = −1; gcd{i¦Aᵢ ≠ = 0} = 1; and (3) f is antipalindromic, i.e., for fpal(x) := x²ⁿf(1/x), we have fpal(x) = −f(x).

Keywords:   number theory, finite field, odd characteristic

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