Some examples of integral definite quaternary quadratic forms with prime discriminant

Class Numbers of Definite Quaternary Forms with Nonsquare Discriminant

2-universal Positive Definite Integral Quinary Quadratic Forms

As a generalization of the famous four square theorem of Lagrange, Ramanujan and Willerding found all positive definite integral quaternary quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary quadratic forms that represent all positive definite integral binary quadratic forms. We also discuss recent results on positive definite int...

2-universal Positive Definite Integral Quinary Diagonal Quadratic Forms

As a generalization of the famous four square theorem of Lagrange, Ramanujan found all positive definite integral quaternary diagonal quadratic forms that represent all positive integers. In this paper, we find all positive definite integral quinary diagonal quadratic forms that represent all positive definite integral binary quadratic forms. §

Gonii: Universal Quaternary Quadratic Forms

We continue our study of quadratic forms using Geometry of Numbers methods by considering universal quaternary positive definite integral forms of square discriminant. We give a small multiple theorem for such forms and use it to prove universality for all nine universal diagonal forms. The most interesting case is x2 + 2y2 + 5z2 + 10w2, which required computer calculations.

On Definite Quadratic Forms, Which Are Not the Sum of Two Definite or Semi-definite Forms

be a positive definite quadratic form with determinant D R and integer coefficients a ;Call it an even form if all a ; ; are even ., an odd form if at least one a ;; is odd . Then Í,, is called non-decomposable, if it cannot be expressed as a sum of two non-negative quadratic forms with integer coefficients . Mordell 1 ) proved that f, can always be decomposed into a sum of five squares of line...