Totally Isotropic Subspaces of Small Height in Quadratic Spaces

Authors

Wai Kiu Chan, Wesleyan University
Lenny Fukshansky, Claremont McKenna CollegeFollow
Glenn Henshaw, LaGuardia Community College

Document Type

Article - postprint

Department

Mathematics (CMC)

Publication Date

2016

Abstract

Let K be a global field or Q, F a nonzero quadratic form on KN , N ≥ 2, and V a subspace of KN . We prove the existence of an infinite collection of finite families of small-height maximal totally isotropic subspaces of (V, F) such that each such family spans V as a K-vector space. This result generalizes and extends a well known theorem of J. Vaaler [16] and further contributes to the effective study of quadratic forms via height in the general spirit of Cassels’ theorem on small zeros of quadratic forms. All bounds on height are explicit.

Comments

Source: Author's post-print manuscript in PDF.

Rights Information

© 2016 Chan, Fukshansky, Henshaw

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Chan, W., Fukshansky, L., Henshaw, G. Totally isotropic subspaces of small height in quadratic spaces, Advances in Geometry, vol. 16 no. 2 (2016), pg. 153--164.