On Hilbert's construction of positive polynomials
Algebraic Geometry
2007-07-17 v1 Number Theory
Abstract
In 1888, Hilbert described how to find real polynomials in more than one variable which take only non-negative values but are not a sum of squares of polynomials. His construction was so restrictive that no explicit examples appeared until the late 1960s. We revisit and generalize Hilbert's construction and present many such polynomials.
Keywords
Cite
@article{arxiv.0707.2156,
title = {On Hilbert's construction of positive polynomials},
author = {Bruce Reznick},
journal= {arXiv preprint arXiv:0707.2156},
year = {2007}
}