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Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
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Jean-Paul Cerri
Published/Copyright:
May 4, 2006
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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- Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
- On the growth rate of the tunnel number of knots
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Articles in the same Issue
- Lines on projective hypersurfaces
- Almost isomorphism for countable state Markov shifts
- Inhomogeneous and Euclidean spectra of number fields with unit rank strictly greater than 1
- On the growth rate of the tunnel number of knots
- Signature homology
- On the structure of cofree Hopf algebras
- Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian
- κ-types and Γ-asymptotic expansions
