Waring's problem for polynomials in two variables

Bodin, Arnaud; Car, Mireille

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1090/S0002-9939-2012-11503-5

Titre :

Waring's problem for polynomials in two variables

Auteur(s) :

Bodin, Arnaud [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Car, Mireille [Auteur]
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

Titre de la revue :

Proceedings of the American Mathematical Society

Pagination :

1577-1589

Éditeur :

American Mathematical Society

Date de publication :

2013-05

ISSN :

0002-9939

Mot(s)-clé(s) en anglais :

several variables polynomials
sum of powers
approximate roots
Vandermonde determinant

Discipline(s) HAL :

Mathématiques [math]/Théorie des nombres [math.NT]

Résumé en anglais : [en]

We prove that all polynomials in several variables can be decomposed as the sums of $k$th powers: $P(x_1,...,x_n) = Q_1(x_1,...,x_n)^k+...+ Q_s(x_1,...,x_n)^k$, provided that elements of the base field are themselves sums ...
Lire la suite >We prove that all polynomials in several variables can be decomposed as the sums of $k$th powers: $P(x_1,...,x_n) = Q_1(x_1,...,x_n)^k+...+ Q_s(x_1,...,x_n)^k$, provided that elements of the base field are themselves sums of $k$th powers. We also give bounds for the number of terms $s$ and the degree of the $Q_i^k$. We then improve these bounds in the case of two variables polynomials of large degree to get a decomposition $P(x,y) = Q_1(x,y)^k+...+ Q_s(x,y)^k$ with $\deg Q_i^k \le \deg P + k^3$ and $s$ that depends on $k$ and $\ln (\deg P)$.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

1104.0472
Accès libre
Accéder au document

Waring's problem for polynomials in two variables BibTeX CSV Excel RIS

Fichiers

Waring's problem for polynomials in two variables

BibTeX

CSV

Excel

RIS