A. Cardoso

collaborators

2 papers

math.NT2026

Metaconjugation and Quadratic Forms

Adriana Cardoso, António Leite, António Machiavelo +2

We present a quaternionic proof that the quadratic form $t^{2} + 2 x^{2} + 5 y^{2} + 10 z^{2}$ represents all positive integers, and that the form $t^{2} + x^{2} + 7 y^{2} + 7 z^{2}$ represents all natural numbers…

math.NT2025

The Dedekind-Hasse Criterion in Quaternion Algebras

Adriana Cardoso, António Machiavelo

We show that a criterion for an integral domain to be a principal ideal domain (PID), due to Dedekind and Hasse, can also be applied in quaternion orders, and that it can be used t…