Document Type
Article
Department
Mathematics (CMC)
Publication Date
2008
Abstract
Let N >= 2 be an integer, F a quadratic form in N variables over (Q) over bar, and Z subset of (Q) over bar (N) 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 (Q) over bar 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 (Q) over bar. We also include some related effective results on orthogonal decomposition and structure of isometries for a bilinear space over (Q) over bar. This extends previous results of the author over number fields. All bounds on height are explicit.
Rights Information
© 2008 World Scientific Publishing Company. http://www.worldscientific.com/
Terms of Use & License Information
Recommended Citation
Fukshansky, Lenny. "Small zeros of quadratic forms over the algebraic closure of Q." International Journal of Number Theory 4.3 (2008): 503-523
Comments
Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,296.
Source: Author's post-print manuscript in pdf