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

• Autorzy: A. Białynicki-Birula , A. Schinzel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 12E05: Polynomials (irreducibility, etc.)
• 11D85: Representation problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 2
• Strony: 201-233

Daty

wydano

2008

Twórcy

autor

A. Białynicki-Birula

• Department of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

A. Schinzel

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm112-2-2