A. Leite

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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

On the Cycle Structure of the Metacommutation Map

AntÃ³nio Leite, AntÃ³nio Machiavelo

Cohn and Kumar showed that the permutation on the set of the classes of left associated Hurwitz primes above an odd prime $p$ induced through metacommutation by a Hurwitz prime $Î¾…