p-adic measures attached to automorphic representations of GL(3)
type: Item
instance of: scholarly article
title: p-adic measures attached to automorphic representations of GL(3)
zbMATH Open document ID: 0656.10023
DOI: 10.1007/BF01393749
published in: Inventiones Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143584
review text: The object of this paper is the L-function that is defined by the symmetric squares of \(\ell\)-adic representations (these form a compatible system of 3-dimensional \(\ell\)-adic representations for the Galois group of \({\bar {\mathbb{Q}}}\) over \({\mathbb{Q}})\). This L-function is interpreted as the twisted L-function of a certain automorphic representation of GL(3). For an ``ordinary'' prime p (i.e. the p-th Fourier coefficient of the corresponding primitive cusp form of weight \(\geq 2\) for the congruence subgroup \(\Gamma_ 0(N)\) is a p-adic unit and p does not divide N) the author constructs a p-adic analogue of this twisted L-function and proves its p-adic holomorphy and functional equation. The essential part of the paper is the p-adic interpolation of all critical values.
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 4071010
zbMATH Keywords: symmetric squares of \(\ell \)-adic representations
zbMATH Keywords: twisted L-function
zbMATH Keywords: automorphic representation of GL(3)
zbMATH Keywords: p-adic holomorphy
zbMATH Keywords: functional equation
zbMATH Keywords: p-adic interpolation
zbMATH Keywords: critical values
author: Claus Günther Schmidt
MaRDI profile type: Publication
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OpenAlex ID: W2018365758
description: scientific article; zbMATH DE number 4071010