• Corpus ID: 118452243

Norm-Euclidean Galois fields

  title={Norm-Euclidean Galois fields},
  author={Kevin J. McGown},
  journal={arXiv: Number Theory},
In this work, we study norm-Euclidean Galois number fields. In the quadratic setting, it is known that there are finitely many and they have been classified. In 1951, Heilbronn showed that for each odd prime l, there are finitely many norm-Euclidean Galois fields of degree l. Unfortunately, his proof does not provide an upper bound on the discriminant, even in the cubic case. We give, for the first time, an upper bound on the discriminant for this class of fields. Namely, for each odd prime l… 
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