Affiliation:
1. Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, Texas 77843-3368, USA
Abstract
Let N ≥ 2 be an integer, F a quadratic form in N variables over [Formula: see text], and [Formula: see text] an L-dimensional subspace, 1 ≤ L ≤ N. We prove the existence of a small-height maximal totally isotropic subspace of the bilinear space (Z,F). This provides an analogue over [Formula: see text] 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 [Formula: see text]. We also include some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over [Formula: see text]. This extends previous results of the author over number fields. All bounds on height are explicit.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Espaces adéliques quadratiques;Mathematical Proceedings of the Cambridge Philosophical Society;2016-06-29
2. Totally isotropic subspaces of small height in quadratic spaces;Advances in Geometry;2016-04-01
3. Height bounds on zeros of quadratic forms over
$$\overline{\mathbb Q}$$
Q
¯;Research in the Mathematical Sciences;2015-09-15
4. Small zeros of quadratic forms outside a union of varieties;Transactions of the American Mathematical Society;2014-04-01
5. Heights and quadratic forms: Cassels’ theorem and its generalizations;Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms;2013