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

Volume 112 / 2008

A. Białynicki-Birula, A. Schinzel Colloquium Mathematicum 112 (2008), 201-233 MSC: 12E05, 11D85. DOI: 10.4064/cm112-2-2


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.


  • A. Białynicki-BirulaDepartment of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
  • A. SchinzelInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21
    00-956 Warszawa, Poland

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