JSTOR Daily

Classification, Construction, and Similitudes of Quadratic Forms

We present a theory of classifying quadratic forms over an algebraic number field which is a reformulation of Eichler's methods and different from the traditional theory of Hasse. As applications we ...
JSTOR Daily

Solving Quadratic Equations Using Reduced Unimodular Quadratic Forms

Let Q be an n x n symmetric matrix with integral entries and with det Q ≠ O, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm ...
Nature

Quadratic Forms and their Classification by Means of Invariant Factors The Axioms of Projective Geometry The Axioms of Descriptive Geometry

THESE are Nos. 3, 4, and 5 of the Cambridge Tracts in Mathematics and Mathematical Physics, which are intended to help students by providing them with brief and readable introductions to mathematical ...
Nature

Identity for the Product of Two Positive Definite Quadratic Forms

THE problem of generalizing the following basic identity given in Hardy, Littlewood and Pólya 1, remains to be considered. We shall show that the generalized Cauchy inequality follows immediately from ...