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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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G2 Examples: the Overall Strategy

G2 Examples: the Overall Strategy

(p.147) Chapter 25 G2 Examples: the Overall Strategy
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This fixes, for each prime p, a prime 𝓁 ≠ p and a choice of nontrivial ℚ¯ℓX-valued additive character ψ‎ of the prime field 𝔽ₚ. Given a finite extension field k/𝔽ₚ, it takes as nontrivial additive character of k the composition k := ψ‎ ○ Trk/𝔽p, whenever a nontrivial additive character of k is (implicitly or explicitly) called for (for instance in the definition of a Kloosterman sheaf, or of a hypergeometric sheaf, on 𝔾ₘ/k).

Keywords:   number theory, nontrivial additive character, Kloosterman sheaf

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