On the Waring problem for polynomial rings.

Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris · Proc Natl Acad Sci U S A · 2012

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Abstract

In this note we discuss an analog of the classical Waring problem for C[x0,x1,...,x(n)]. Namely, we show that a general homogeneous polynomial p ∈ C[x0,x1,...,x(n)] of degree divisible by k≥2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x0,x1,...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.