# The shapes of Galois quartic fields

@article{Piper2019TheSO, title={The shapes of Galois quartic fields}, author={H Piper and Robert Harron}, journal={arXiv: Number Theory}, year={2019} }

We determine the shapes of all degree $4$ number fields that are Galois. These lie in four infinite families depending on the Galois group and the tame versus wild ramification of the field. In the $V_4$ case, each family is a two-dimensional space of orthorhombic lattices and we show that the shapes are equidistributed, in a regularized sense, in these spaces as the discriminant goes to infinity (with respect to natural measures). We also show that the shape is a complete invariant in some… Expand

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