The residual spectrum of \(Sp(2)\)
type: Item
instance of: scholarly article
title: The residual spectrum of \(Sp(2)\)
zbMATH Open document ID: 0833.11018
author: Takuya Konno
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-12-19T00:00:00Z
review text: Let \(G\) be the rank two symplectic group \(\text{Sp} (2)\) over a number field \(k\), and let \(A\) be the adele ring of \(k\). The space of \(L^2\) automorphic forms on \(G(k) \setminus G(A)\) decomposes into a direct sum of the discrete spectrum \(L^2_{\text{disc}}\) and the continuous spectrum \(L^2_{\text{const}}\). The cuspidal spectrum \(L^2_{\text{cusp}}\) is contained in \(L^2_{\text{disc}}\). The orthogonal complement of the cuspidal spectrum in the discrete spectrum is called the residual spectrum. The author obtains the irreducible decomposition of the residual spectrum when \(k\) is totally real.
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 22E55
zbMATH DE Number: 701483
zbMATH Keywords: rank two symplectic group
zbMATH Keywords: automorphic forms
zbMATH Keywords: residual spectrum
zbMATH Keywords: irreducible decomposition
reviewed by: Yangbo Ye
MaRDI profile type: Publication
full work available at URL: pjaa.70.204
OpenAlex ID: W2091406795
cites work: Q3868004
cites work: On the degree 5 \(L\)-function for \(Sp(2)\)
cites work: Spectral decomposition and Eisenstein series
DOI: 10.3792/PJAA.70.204
description: scientific article; zbMATH DE number 701483