Mathematics – Number Theory
Scientific paper
2005-12-06
International Journal of Number Theory, vol. 4 no. 3 (2008), pg. 503-523
Mathematics
Number Theory
17 pages; revised version per referee's request, in particular section 6 has been largely expanded; to appear in the Internati
Scientific paper
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.
No associations
LandOfFree
Small zeros of quadratic forms over the algebraic closure of Q does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Small zeros of quadratic forms over the algebraic closure of Q, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small zeros of quadratic forms over the algebraic closure of Q will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-697958