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 ([20]) in the case of mixed signature in order to get explicit bounds for the Euclidean minimum. (C) 2016 Elsevier Inc. All rights reserved.


Published in:
Journal Of Number Theory, 167, 88-103
Year:
2016
Publisher:
San Diego, Academic Press Inc Elsevier Science
ISSN:
0022-314X
Keywords:
Laboratories:




 Record created 2016-07-19, last modified 2018-09-13


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