Quasi-genera of quadratic forms

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.

One class genera of ternary quadratic forms over number fields

We enumerate all one class genera of definite ternary quadratic forms over number fields. For this, we construct all Gorenstein orders of type number one in definite quaternion algebras over number fields. Finally, we list all definite quaternion orders of ideal class number one.

One-class genera of maximal integral quadratic forms

Suppose Q is a definite quadratic form on a vector space V over some totally real field K 6= Q. Then the maximal integral ZK-lattices in (V,Q) are locally isometric everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q) of dimension at least 3, where the corresponding genus of maximal integral lattices consists of a single isometry class. It turns out, there are 469 ...

Exceptional Integers for Genera of Integral Ternary Positive Definite Quadratic Forms

0. Introduction. In [2] it was shown that in a certain sense most integers represented by some form in the genus of a given integral ternary positive definite quadratic form are represented by all forms in this genus. More precisely, let (L,q) be a Zlattice of rank 3 with integral positive definite quadratic form. Then all sufficiently large integers a that are represented primitively by some l...

Representation of Quadratic Forms by Integral Quadratic Forms