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Binary hermitian forms and optimal embeddings
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Fix a quadratic order over the ring of integers. An embedding of the quadratic order into a quaternionic order naturally gives an integral binary hermitian form over the quadratic order. We show that, in certain cases, this correspondence is a discriminant preserving bijection between the isomorphism classes of embeddings and integral binary hermitian forms.
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Extensions of integral orthoregular sets and icubes
Every Gaussian-integer icube in dimension 4, and every one in dimension 3 whose norm is a sum of two squares, extends to an equal-length integral orthogonal basis; in dimension 4k+2 the norm must be a sum of two squares.
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