On the Waring problem for polynomial rings.
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- Record sourced from PubMed, PMID 22460787.
- Also identified by DOI 10.1073/pnas.1120984109 and PMC identifier 3326489.
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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.