Quadratic Forms of Height Two

Quadratic Forms and Height Functions

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

The Minimal Height of Quadratic Forms of given Dimension

Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fields of characteristic = 2 and prove that the height of an n-dimensional excellent form (depending on n only) is the (precise) lower bound of the heights of all forms of dimension n.

Height Bounds on Zeros of Quadratic Forms Over Q-bar

In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For a single quadratic form in N ≥ 2 variables on a subspace of Q , we prove an upper bound on the height of a smallest nontrivial zero outside of an algebraic set under the assumption that such a zero exists. For a system of k quadratic forms on an L-dimensional subspace of Q , N ≥ L ≥ k(k+1) 2 + 1,...

Representation of Quadratic Forms by Integral Quadratic Forms