Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\)
type: Item
instance of: scholarly article
title: Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\)
zbMATH Open document ID: 1443.11079
author: Olof Ahlén
author: Henrik P. A. Gustafsson
author: Axel Kleinschmidt
author: Baiying Liu
author: Daniel Persson
published in: Journal of Number Theory
publication date: 2018-09-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1707.08937
review text: The authors show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of \(\mathrm{SL}_n(\mathbb A)\) are completely determined by certain highly degenerate Whittaker coefficients. They give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, they derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have possible applications for scattering amplitudes in string theory.
reviewed by: Goran Muić
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 6943089
zbMATH Keywords: small automorphic forms
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Fourier expansion
MaRDI profile type: Publication
OpenAlex ID: W2802676600
arXiv ID: 1707.08937
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DOI: 10.1016/J.JNT.2018.03.022
description: scientific article