Inhomogeneous minima of mixed signature lattices
We 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 () in the case of mixed signature in order to get explicit bounds for the Euclidean minimum. (C) 2016 Elsevier Inc. All rights reserved.