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

### Volume 112 / 2008

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

#### 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.