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On the Euclidean minimum of some real number fields

Eva Bayer-Fluckiger, Gabriele Nebe (2005)

Journal de Théorie des Nombres de Bordeaux

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.

On the existence of Minkowski units in totally real cyclic fields

František Marko (2005)

Journal de Théorie des Nombres de Bordeaux

Let K be a totally real cyclic number field of degree n that is the product of two distinct primes and such that the class number of the n -th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for K .

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