THE DENSITY OF INTEGRAL QUADRATIC FORMS HAVING A k-DIMENSIONAL TOTALLY ISOTROPIC SUBSPACE
Abstract
We investigate the probability that a random quadratic form in Z[x1,…,xn] has a totally isotropic subspace of a given dimension. We show that this global probability is a product of local probabilities. Our main result computes these local probabilities for quadratic forms over the p-adics. The formulae we obtain are rational functions in p invariant upon substituting p↦1/p.
Fields of Study & Subjects
advanced mathematical theories
Mathematical Dynamics and Fractals
Geometry and complex manifolds
Publication details
- Journal / source
- Rocky Mountain Journal of Mathematics
- Volume
- 56
- Issue
- 2
- Pages
- 403–421
- Publication date
- 1 April 2026
- Language
- EN