On the Waring problem for polynomial rings

Details On the Waring problem for polynomial rings On the Waring problem for polynomial rings

2011-12-06

arxiv.org/abs/1112.1371v1

Mathematics

Algebraic Geometry

6 pages

Scientific paper

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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