Constants as sums of polynomial cubes in characteristic 2
type: Item
instance of: scholarly article
zbMATH Open document ID: 1308.11102
author: Luis Gallardo
author: L. N. Vaserstein
publication date: 2013-12-30T00:00:00Z
Mathematics Subject Classification ID: 11T55
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 6242291
MaRDI profile type: Publication
Recommended article: On polynomials that are sums of two cubes
Recommended article: Sums of Cubes in Polynomial Rings
Recommended article: Cubic Character Sums of Cubic Polynomials
Recommended article: SUMS OF CUBES AND SQUARES OF POLYNOMIALS WITH COEFFICIENTS IN A FINITE FIELD
Recommended article: Sums of cubes of polynomials
Recommended article: SOME CHARACTER SUMS OF THE POLYNOMIALS
Recommended article: Characterization of quadratic and cubic \(\sigma\)-polynomials
Recommended article: The Representation of Integers as Sums of Values of Cubic Polynomials. II
Recommended article: Note on character sums of Hilbert cubes
Recommended article: CERTAIN CUBIC POLYNOMIALS OVER FINITE FIELDS
title: Constants as sums of polynomial cubes in characteristic 2
published in: Journal of Combinatorics and Number Theory
review text: In a finite field \(\mathbb{F}_q\) any element can be represented as the sum of two squares or three cubes (except for \(q=4\)) of elements of \(\mathbb{F}_q\). The authors consider the similar problem of representing the elements of \(\mathbb{F}_q\) as the sums of squares or cubes of polynomials of one variable over \(\mathbb{F}_q\) when at least one of the polynomials is nonconstant.NEWLINENEWLINEIt is shown that for any \(q\) all elements of the finite field \(\mathbb{F}_q\) can be written as the sum of squares of at least three elements from \(\mathbb{F}_q[t]\). Also partial results are given for the representation as the sum of cubes of polynomials for the characteristic 2 case.
reviewed by: Ayça Çeşmelioğlu
description: scientific article; zbMATH DE number 6242291