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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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Autodualities and Signs

Autodualities and Signs

(p.49) Chapter 9 Autodualities and Signs
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter takes up the proofs of Theorems 9.1 and 9.2. Theorem 9.1: Suppose that N in Garith is geometrically irreducible, ι‎-pure of weight zero, and arithmetically self-dual. Denote by ɛ the sign of its autoduality. For variable finite extension fields E/k, we have the estimate for ɛ. Theorem 9.2: Suppose that that N in Garith is geometrically irreducible (so a fortiori arithmetically irreducible) and ι‎-pure of weight zero.

Keywords:   number theory, autoduality, signs

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