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math.NT2019★ 1 cited
The shapes of Galois quartic fields
Piper H, Robert Harron
We determine the shapes of all degree number fields that are Galois. These lie in four infinite families depending on the Galois group and the tame versus wild ramification of…
math.NT2019★ 3 cited
Equidistribution of shapes of complex cubic fields of fixed quadratic resolvent
Robert Harron
We show that the shape of a complex cubic field lies on the geodesic of the modular surface defined by the field's trace-zero form. We also prove a general such statement for all o…