Norm-euclidean Cyclic Fields of Prime Degree
نویسنده
چکیده
Let K be a cyclic number field of prime degree `. Heilbronn showed that for a given ` there are only finitely many such fields that are normEuclidean. In the case of ` = 2 all such norm-Euclidean fields have been identified, but for ` 6= 2, little else is known. We give the first upper bounds on the discriminants of such fields when ` > 2. 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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