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arXiv · 1112.1371

On the Waring problem for polynomial rings

Ralf Fröberg·Giorgio Ottaviani·Boris Shapiro
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Abstract

In this note we discuss an analog of the classical Waring problem for C[x_0, x_1,...,x_n]. Namely, we show that a general homogeneous polynomial p \in C[x_0,x_1,...,x_n] of degree divisible by k\ge 2 can be represented as a sum of at most k^n k-th powers of homogeneous polynomials in C[x_0, x_1,...,x_n]. Noticeably, k^n coincides with the number obtained by naive dimension count.

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Ralf Fröberg, Giorgio Ottaviani, Boris Shapiro. 2011-12-06. On the Waring problem for polynomial rings. https://doi.org/10.1073/pnas.1120984109

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