On the Waring problem for polynomial rings
Algebraic Geometry
2015-06-03 v1 Commutative Algebra
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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Cite
@article{arxiv.1112.1371,
title = {On the Waring problem for polynomial rings},
author = {Ralf Fröberg and Giorgio Ottaviani and Boris Shapiro},
journal= {arXiv preprint arXiv:1112.1371},
year = {2015}
}
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6 pages