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Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1

  • Jean-Paul Cerri EMAIL logo
Published/Copyright: May 4, 2006
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Journal für die reine und angewandte Mathematik
From the journal Volume 2006 Issue 592

Abstract

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.

Received: 2004-06-14
Revised: 2005-02-21
Published Online: 2006-05-04
Published in Print: 2006-03-24

© Walter de Gruyter

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