Bounds for exponential sums over finite fields
type: Item
instance of: scholarly article
title: Bounds for exponential sums over finite fields
zbMATH Open document ID: 0834.11055
author: Valérie Gillot
published in: Finite Fields and their Applications
publication date: 1996-02-07T00:00:00Z
review text: This paper is concerned with exponential sums defined over finite fields \(\mathbb{F}_{q^s}\), where \(q\) is a power of a prime. Such a sum involving a polynomial \(f(x)\) of one variable is transformed into a sum over \(\mathbb{F}_q\), by substituting \(x= x_1 b_1+ \dots+ x_s b_s\), where \(b_1, \dots, b_s\) is a vector space basis for \(\mathbb{F}_{q^s}\) over \(\mathbb{F}_q\). This produces a new polynomial in \(s\) variables, to which Deligne's bounds may be applied. In certain cases this leads to results superior to those following from Weil's estimate. The method is also applied to diagonal forms in more than one variable.
reviewed by: D. R. Heath-Brown
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 828731
zbMATH Keywords: polynomial in several variables
zbMATH Keywords: exponential sums
zbMATH Keywords: finite fields
zbMATH Keywords: diagonal forms
MaRDI profile type: Publication
full work available at URL: ffta.1995.1033
OpenAlex ID: W1977166565
DOI: 10.1006/FFTA.1995.1033
description: scientific article; zbMATH DE number 828731