Jean-Paul Cerri
Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
Let K be a number field with unit rank r > 1. In this article we show that the inhomogeneous minimum
of K is attained by at least one rational point. In particular, if M(K) is the Euclidean minimum of K, we have
. This phenomenon has consequences on the decidability of the Euclidean nature of such a field. Moreover, in case K is not a CM-field, we prove that
is attained, isolated, and that the inhomogeneous minimum function takes discrete rational values.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 03/2006
Pages: 49 - 62
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