Tom Fisher's Home Page

joint with Lycka Drakengren

We investigate the probability that a random quadratic form in Z[x₁, ... , x_n] 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.

The density of integral quadratic forms having a k-dimensional totally isotropic subspace   (19 pages)          

---