Representations of multivariate polynomials by sums of univariate polynomials in linear forms

A. Białynicki-Birula, and A. Schinzel. "Representations of multivariate polynomials by sums of univariate polynomials in linear forms." Colloquium Mathematicae 112.2 (2008): 201-233. <http://eudml.org/doc/283733>.

@article{A2008,
abstract = {The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and degree is given. Also some special cases of these problems are studied.},
author = {A. Białynicki-Birula, A. Schinzel},
journal = {Colloquium Mathematicae},
keywords = {Polynomials; representation of a multivariate polynomial; sums of powers of linear polynomials and forms; Waring problem},
language = {eng},
number = {2},
pages = {201-233},
title = {Representations of multivariate polynomials by sums of univariate polynomials in linear forms},
url = {http://eudml.org/doc/283733},
volume = {112},
year = {2008},
}

TY - JOUR
AU - A. Białynicki-Birula
AU - A. Schinzel
TI - Representations of multivariate polynomials by sums of univariate polynomials in linear forms
JO - Colloquium Mathematicae
PY - 2008
VL - 112
IS - 2
SP - 201
EP - 233
AB - The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and degree is given. Also some special cases of these problems are studied.
LA - eng
KW - Polynomials; representation of a multivariate polynomial; sums of powers of linear polynomials and forms; Waring problem
UR - http://eudml.org/doc/283733
ER -