\(L\) functions of some exponential sums of finite classical groups
type: Item
instance of: scholarly article
title: \(L\) functions of some exponential sums of finite classical groups
zbMATH Open document ID: 1040.11060
author: Hi-joon Chae
author: Dae San Kim
published in: Mathematische Annalen
publication date: 2003-09-16T00:00:00Z
review text: The authors consider exponential sums \(E_n(V,f)\) and the \(L\) function \(L(t,V,f)\) associated to a variety \(V\), a regular function \(f\) on it and a fixed nontrivial additive character \(\lambda\) of \({\mathbb F}_q\). They give a formula for the exponential sum \(\sum_{g\in G} \lambda(\text{tr}\, g)\) as the alternating sum of traces of the Frobenius map acting on a Weyl group invariant for certain cohomology groups of \((G/T)\times T\), where \(T\) is a maximal torus of \(G\). Explicit computations are given for the classical groups \(\text{GL}_n\), \(\text{SL}_n\) and \(\text{Sp}_{2n}\). In these cases the \(L\) functions are explicitly described. The the exponential sum \(\sum_{g\in \text{GL}_n({\mathbb F}_q)} \,\lambda(\text{tr}\,g + \text{tr}\, g^{-1}) \) is also computed.
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 11T23
zbMATH DE Number: 1982579
zbMATH Keywords: \(L\) functions
zbMATH Keywords: exponential sums
zbMATH Keywords: classical groups
MaRDI profile type: Publication
full work available at URL: s00208-003-0431-z
OpenAlex ID: W1525194791
DOI: 10.1007/S00208-003-0431-Z
description: scientific article; zbMATH DE number 1982579