Totally isotropic subspaces of small height in quadratic spaces

2014/09/16 by Wai Kiu Chan, Lenny Fukshansky, Chan, Wai Kiu +3
Mathematics · #11E12 #11G50 #11H06 #Algebraic Geometry and Number Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1409.4717

openalex publication_date 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a global field or \mathbb Q, F a nonzero quadratic form on K^N, N ≥ 2, and V a subspace of K^N. 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 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.

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