Bayer-Fluckiger, EvaBorello, MartinoJossen, Peter2016-07-192016-07-192016-07-19201610.1016/j.jnt.2016.03.010https://infoscience.epfl.ch/handle/20.500.14299/127501WOS:000377056400005We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([9-11]). In the case of totally real fields, an optimal bound was conjectured by Minkowski and it is proved for fields of small degree. In this note we develop methods of McMullen ([20]) in the case of mixed signature in order to get explicit bounds for the Euclidean minimum. (C) 2016 Elsevier Inc. All rights reserved.LatticesEuclidean minimumInhomogeneous minima of mixed signature latticestext::journal::journal article::research article