Quadratic forms with cube-free discriminant

Polynomial bounds for equivalence of quadratic forms with cube - free determinant

Given two integrally equivalent integral quadratic forms in at least three variables and with cube-free determinant, we establish an upper bound on the smallest unimodular matrix transforming one of the forms into the other. This bound is polynomial in the height of the two forms involved, confirming a conjecture of Masser for the class of forms considered.

A Probabilistic Factorization Algorithm with Quadratic Forms of Negative Discriminant

We propose a probabilistic algorithm for factorization of an integer N with run time (exp^log/V loglogJV)/5/4"1""'1'. Asymptotically, our algorithm will be as fast as the wellknown factorization algorithm of Morrison and Brillhart. The latter algorithm will fail in several cases and heuristic assumptions are needed for its run time analysis. Our new algorithm will be analyzed under the assumpti...

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.

Bayesian Quadratic Discriminant Analysis

Quadratic discriminant analysis is a common tool for classification, but estimation of the Gaussian parameters can be ill-posed. This paper contains theoretical and algorithmic contributions to Bayesian estimation for quadratic discriminant analysis. A distribution-based Bayesian classifier is derived using information geometry. Using a calculus of variations approach to define a functional Bre...

Representation of Quadratic Forms by Integral Quadratic Forms