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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: Construction in Characteristic Two

G2 Examples: Construction in Characteristic Two

(p.155) Chapter 26 G2 Examples: Construction in Characteristic Two
Convolution and Equidistribution

Nicholas M. Katz

Princeton University Press

This chapter treats the case of characteristic two separately because it is somewhat simpler than the case of odd characteristic. Recall from the first paragraph of Chapter 25 that for k a finite field of characteristic 2, and any character χ‎ of kË£, the Tate-twisted Kloosterman sheaf of rank seven has Ggeom = Garith = Gâ‚‚. The first task is to express its stalk at a fixed point a É› kË£ as the finite field Mellin transform of the desired object N(a; k).

Keywords:   number theory, characteristic two, Kloosterman sheaf, finite field Mellin transform

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