Geodesic
Representations of multivariate polynomials by sums of univariate polynomials in linear forms
A. Białynicki-Birula 1   ; A. Schinzel 2
1 Department of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland
Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 201-233 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm112-2-2
Keywords: paper concentrated issues presentation multivariate polynomial field necessarily algebraically closed sum univariate polynomials linear forms defined presentation form particular zero form sum powers linear forms projectively distinct defined algebraically closed field upper bound number summands presentations only generic polynomials forms given number variables degree given special cases these problems studied

A. Białynicki-Birula  1   ; A. Schinzel  2

1 Department of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences P.O. Box 21 00-956 Warszawa, Poland 
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A. Białynicki-Birula; A. Schinzel. Representations of multivariate polynomials by
 sums of univariate polynomials in linear forms. Colloquium Mathematicum, Tome 112 (2008) no. 2, pp. 201-233. doi: 10.4064/cm112-2-2

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