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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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SL(n) Examples with Slightly Composite n

SL(n) Examples with Slightly Composite n

(p.135) Chapter 22 SL(n) Examples with Slightly Composite n
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter continues to study the object N of Theorem 21.1. Thus, k is a finite field of characteristic p, ψ‎ a nontrivial additive character of k, f(x) = f(x)=∑i=−baAixi∈k[x,1/x]Axⁱ ɛ k[x, 1/x] is a Laurent polynomial of “bidegree” (a, b), with a; b both ≤ 1 and both prime to p. It is assumed that f(x) is Artin–Schreier reduced. It takes for N the object N:ℒψ(f(x))(1/2)[1]∈ρarith.

Keywords:   number theory, Laurent polynomial, Artin–Schreier reduced polynomial

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