Small zeros of quadratic forms over the algebraic closure of Q
| dc.creator | Fukshansky, Lenny | |
| dc.date | 2005-12-06 | |
| dc.date | 2007-03-21 | |
| dc.date.accessioned | 2026-07-07T09:57:11Z | |
| dc.date.available | 2026-07-07T09:57:11Z | |
| dc.description | Let $N \geq 2$ be an integer, $F$ a quadratic form in $N$ variables over $\bar{\mathbb Q}$, and $Z \subseteq \bar{\mathbb Q}^N$ an $L$-dimensional subspace, $1 \leq L \leq N$. We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space $(Z,F)$. This provides an analogue over $\bar{\mathbb Q}$ of a well-known theorem of Vaaler proved over number fields. We use our result to prove an effective version of Witt decomposition for a bilinear space over $\bar{\mathbb Q}$. We also include some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over $\bar{\mathbb Q}$. This extends previous results of the author over number fields. All bounds on height are explicit. | |
| dc.description | 17 pages; revised version per referee's request, in particular section 6 has been largely expanded; to appear in the International Journal of Number Theory | |
| dc.identifier | https://arxiv.org/abs/math/0512132 | |
| dc.identifier | http://arxiv.org/abs/math/0512132 | |
| dc.identifier | International Journal of Number Theory, vol. 4 no. 3 (2008), pg. 503-523 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167250 | |
| dc.subject | Number Theory | |
| dc.subject | 11E12, 11G50, 11H55, 11D09 | |
| dc.title | Small zeros of quadratic forms over the algebraic closure of Q | |
| dc.type | text |