The shapes of pure cubic fields

@article{Harron2015TheSO,
  title={The shapes of pure cubic fields},
  author={Robert Harron},
  journal={arXiv: Number Theory},
  year={2015}
}
  • R. Harron
  • Published 4 September 2015
  • Mathematics
  • arXiv: Number Theory
We determine the shapes of pure cubic fields and show that they fall into two families based on whether the field is wildly or tamely ramified (of Type I or Type II in the sense of Dedekind). We show that the shapes of Type I fields are rectangular and that they are equidistributed, in a regularized sense, when ordered by discriminant, in the one-dimensional space of all rectangular lattices. We do the same for Type II fields, which are however no longer rectangular. We obtain as a corollary of… 
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