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.
Binary hermitian forms and optimal embeddings
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.NT 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.