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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On Humbert-Minkowski's constant
for a number field

Authors: R. Baeza and M. I. Icaza
Journal: Proc. Amer. Math. Soc. 125 (1997), 3195-3202
MSC (1991): Primary 11E12, 11H50; Secondary 11R29, 15A48
MathSciNet review: 1403112
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Abstract | References | Similar Articles | Additional Information

Abstract: We use Humbert's reduction theory to introduce an obstruction for the unimodularity of minimal vectors of positive definite quadratic forms over totally real number fields. Using this obstruction we obtain an inequality relating the values of a generalized Hermite constant for such fields, which over the field of rational numbers leads to a well-known result of Mordell.

References [Enhancements On Off] (What's this?)

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Additional Information

R. Baeza
Affiliation: Department of Mathematics, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago-Chile
Email: rbaeza@abello.dic.uchile.cle

M. I. Icaza
Affiliation: Department of Mathematics, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago-Chile
Email: icazap@abello.dic.uchile.cle

PII: S 0002-9939(97)03940-3
Keywords: Quadratic forms, Hermite constant, reduction theory.
Received by editor(s): January 18, 1996
Received by editor(s) in revised form: June 13, 1996
Additional Notes: The first author was partially supported by Fondecyt 1950392 and European Union # CI1*-CT93-0353
The second author was supported by Fondecyt 3940002 and European Union # CI1*-CT93-0353
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society

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