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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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GL(n) × GL(n) × … × GL(n) Examples

GL(n) × GL(n) × … × GL(n) Examples

Chapter:
(p.113) Chapter 20 GL(n) × GL(n) × … × GL(n) Examples
Source:
Convolution and Equidistribution
Author(s):

Nicholas M. Katz

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153308.003.0021

This chapter investigates the question which begings as follows. Suppose we have a geometrically irreducible middle extension sheaf G on 𝔾ₘ/k which is pure of weight zero, such that the object N := G(1/2)[1] ɛ Garith is “dimension” n and has Gsubscript geom,N = Garith,N = GL(n). Suppose in addition we are given s ≤ 2 distinct characters χ‎ᵢ of kˣ.

Keywords:   number theory, middle extension sheaf, geometrical irreducibility

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