An \(\widehat{A_4}\) extension of \({\mathbb{Q}}\) attached to a non-selfdual automorphic form on \(GL(3)\)
type: Item
instance of: scholarly article
title: An \(\widehat{A_4}\) extension of \({\mathbb{Q}}\) attached to a non-selfdual automorphic form on \(GL(3)\)
zbMATH Open document ID: 0713.11036
DOI: 10.1007/BF01445238
author: Avner Ash
author: Richard Pinch
author: Richard Taylor
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164897
review text: Clozel has conjectured that an algebraic automorphic representation of GL(n) over \({\mathbb{Q}}\) has attached to it a compatible system of \(\lambda\)- adic representations of Gal(\({\bar {\mathbb{Q}}}/{\mathbb{Q}})\). When the automorphic representation is not essentially-selfdual no approaches to prove the conjecture or even examples of it are known. We provide modular numerical evidence for the truth of the conjecture in one instance, where \(\lambda =\sqrt{-3}\) and the automorphic representation occurs in the cohomology of a congruence subgroup of level 61 in GL(3,\({\mathbb{Z}})\).
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 4173089
zbMATH Keywords: Clozel conjecture
zbMATH Keywords: non-selfdual automorphic form
zbMATH Keywords: automorphic representation
Wikidata QID: Q116217876
MaRDI profile type: Publication
cites work: Computations of cuspidal cohomology of congruence subgroups of SL(3,\({\mathbb{Z}})\)
cites work: Q3484924
cites work: Explicit construction of \(\tilde A_ n\) type fields
cites work: Méthodes et algorithmes pour le calcul numérique du nombre de classes et de unités des extensions cubiques cycliques de Q.
cites work: The Witt invariant of the form \(\text{Tr}(x^ 2)\)
cites work: Q5625265
OpenAlex ID: W2914251160
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description: scientific article; zbMATH DE number 4173089