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Norm-Euclidean Galois fields
Let K be a Galois number field of prime degree . Heilbronn showed that
for a given there are only finitely many such fields that are
norm-Euclidean. In the case of all such norm-Euclidean fields have
been identified, but for , little else is known. We give the first
upper bounds on the discriminants of such fields when . Our methods
lead to a simple algorithm which allows one to generate a list of candidate
norm-Euclidean fields up to a given discriminant, and we provide some
computational results
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