On the absence of uniform denominators in Hilbert's 17th problem
| dc.creator | Reznick, Bruce | |
| dc.date | 2003-06-10 | |
| dc.date.accessioned | 2026-07-07T04:58:43Z | |
| dc.date.available | 2026-07-07T04:58:43Z | |
| dc.description | Hilbert showed that for most $(n,m)$ there exist psd forms $p(x_1,...,x_n)$ of degree $m$ which cannot be written as a sum of squares of forms. His 17th problem asked whether, in this case, there exists a form $h$ so that $h^2p$ is a sum of squares of forms; that is, $p$ is a sum of squares of rational functions with denominator $h$. We show that, for every such $(n,m)$ there does not exist a single form $h$ which serves in this way as a denominator for {\it every} psd $p(x_1,...,x_n)$ of degree $m$. | |
| dc.description | Submitted to Proceedings of the American Mathematical Society | |
| dc.identifier | https://arxiv.org/abs/math/0306163 | |
| dc.identifier | http://arxiv.org/abs/math/0306163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67752 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Number Theory | |
| dc.subject | 11E10, 11E25, 11E76, 12D15, 14P99 | |
| dc.title | On the absence of uniform denominators in Hilbert's 17th problem | |
| dc.type | text |