On the Waring problem for polynomial rings

In this note we discuss an analog of the classical Waring problem for Formula . Namely, we show that a general homogeneous polynomial Formula of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in Formula . Noticeably, kn coincides with the num...

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Veröffentlicht in:	Proceedings of the National Academy of Sciences - PNAS 2012-04, Vol.109 (15), p.5600-5602
Hauptverfasser:	Fröberg, Ralf, Ottaviani, Giorgio, Shapiro, Boris
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Degrees of polynomials equations Geometry Hyperplanes Induction assumption Integers Mathematical inequalities Mathematical problems Mathematical rings Physical Sciences Polynomials Secant function sum of powers sum of squares topology Veronese embedding
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Zusammenfassung:	In this note we discuss an analog of the classical Waring problem for Formula . Namely, we show that a general homogeneous polynomial Formula of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in Formula . Noticeably, kn coincides with the number obtained by naive dimension count.
ISSN:	0027-8424 1091-6490 1091-6490
DOI:	10.1073/pnas.1120984109