Similarity of Quadratic Forms and Half-Neighbors

Neighbors of Indefinite Binary Quadratic Forms

In this paper, we derive some algebraic identities on right and left neighbors R(F ) and L(F ) of an indefinite binary quadratic form F = F (x, y) = ax + bxy + cy of discriminant Δ = b − 4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F . Keywords—Quadratic form, indefinite form, cy...

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.

Comparison of the main forms of half-quadratic regularization

On a Conjecture of Izhboldin on Similarity of Quadratic Forms

In his paper Motivic equivalence of quadratic forms , Izhboldin modi es a conjecture of Lam and asks whether two quadratic forms, each of which isomorphic to the product of an Albert form and a k-fold P ster form, are similar provided they are equivalent modulo I k+3 . We relate this conjecture to another conjecture on the dimensions of anisotropic forms in I k+3 . As a consequence, we obtain t...

Representation of Quadratic Forms by Integral Quadratic Forms