Sums of squares over totally real fields are rational sums of squares
| dc.creator | Hillar, Christopher J. | |
| dc.date | 2007-04-21 | |
| dc.date | 2008-08-29 | |
| dc.date.accessioned | 2026-07-07T09:58:55Z | |
| dc.date.available | 2026-07-07T09:58:55Z | |
| dc.description | Let $K$ be a totally real number field with Galois closure $L$. We prove that if $f \in \mathbb Q[x_1,...,x_n]$ is a sum of $m$ squares in $K[x_1,...,x_n]$, then $f$ is a sum of \[4m \cdot 2^{[L: \mathbb Q]+1} {[L: \mathbb Q] +1 \choose 2}\] squares in $\mathbb Q[x_1,...,x_n]$. Moreover, our argument is constructive and generalizes to the case of commutative $K$-algebras. This result gives a partial resolution to a question of Sturmfels on the algebraic degree of certain semidefinite programing problems. | |
| dc.description | 10 pages, final version to appear in Proceedings of the AMS | |
| dc.identifier | https://arxiv.org/abs/0704.2824 | |
| dc.identifier | http://arxiv.org/abs/0704.2824 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167860 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Optimization and Control | |
| dc.subject | Rings and Algebras | |
| dc.title | Sums of squares over totally real fields are rational sums of squares | |
| dc.type | text |