A spectral mean value theorem for \(\text{GL}(3)\)
type: Item
instance of: scholarly article
title: A spectral mean value theorem for \(\text{GL}(3)\)
zbMATH Open document ID: 1208.11070
author: Xiaoqing Li
published in: Journal of Number Theory
publication date: 2010-10-19T00:00:00Z
review text: Let \(\{\phi_j\}\) be an orthonormal basis of Maaß forms for \(\text{SL}(3,{\mathbb Z})\), and \(W_j^{(1,1)}(y)\) be the first Fourier coefficient of \(\phi_j\). The paper gives a bound on the averages of \(|W_j^{(1,1)}(y)|^2\) over certain subsets of the cuspidal spectrum of \(\text{SL}(3)\), when \(y\) is a fixed diagonal matrix that is sufficiently dominant. The proof is an elegant application of Kuznetsov formula in \(\text{SL}(3)\) case, which is much more complex than the formula in \(\text{SL}(2)\) case.
reviewed by: Zhengyu Mao
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11F37
zbMATH DE Number: 5802561
zbMATH Keywords: Kuznetsov formula
zbMATH Keywords: Kloosterman sum
zbMATH Keywords: Weyl law
describes a project that uses: GL(n)pack
MaRDI profile type: Publication
full work available at URL: j.jnt.2010.04.008
OpenAlex ID: W2014710845
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DOI: 10.1016/J.JNT.2010.04.008
description: scientific article; zbMATH DE number 5802561