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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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Orthogonal Examples, Especially SO(n) Examples

Orthogonal Examples, Especially SO(n) Examples

Chapter:
(p.103) Chapter 19 Orthogonal Examples, Especially SO(n) Examples
Source:
Convolution and Equidistribution
Author(s):

Nicholas M. Katz

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153308.003.0020

The orthogonal case is more diffcult than the symplectic one because of the need to distinguish between SO(n) and O(n), which we do not in general know how to do. This chapter works on either the split or the nonsplit form. It begins with a lisse sheaf Ƒ on a dense open set j : UG which is geometrically irreducible, pure of weight zero, and not geometrically isomorphic to (the restriction to U of) any Kummer sheaf Lᵪ. It denotes by G := j*Ƒ its middle extension to G. Then the object N := G(1/2)[1] ɛ Garith is pure of weight zero and geometrically irreducible. The result is the orthogonal version of Theorem 18.1.

Keywords:   number theory, split form, nonsplit form, orthogonal case

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