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On Humbert-Minkowski's constant for a number field

Author(s): R. Baeza; M. I. Icaza
Journal: Proc. Amer. Math. Soc. 125 (1997), 3195-3202.
MSC (1991): Primary 11E12, 11H50; Secondary 11R29, 15A48
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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:

[B]
Baeza, R.: The volume of the space of Humbert reduced forms. Preprint. Universidad de Chile, 1994.

[C-S]
Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften 290, Springer, 1988. MR 89a:11067

[Fr]
Freitag, E.: Hilbert Modular Forms. Springer-Verlag (1990). MR 91c:11025

[I]
Icaza, M.I.: Hermite constant and extreme forms for algebraic number fields. To appear in Journal of London Math. Soc. (2) 55, 11-22, 1997. CMP 97:05

[H]
Humbert, P.: Thèorie de la reduction des formes quadratiques dèfinies positives dans un corps algebrique $ \; K \; $ finie. Com. Math. Helv. 12, 263-306, 1939-1940. MR 2:148a

[OM]
O'Meara, O.T.: Introduction to Quadratic Forms. Grundlehren Math. Wiss Bd. 117, Springer-Verlag (1963). MR 27:2485

[Si]
Siegel, C.L.: Lectures on the Geometry of Numbers, Springer-Verlag. 1988. MR 91d:11070

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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

DOI: 10.1090/S0002-9939-97-03940-3
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
Copyright of article: Copyright 1997, American Mathematical Society

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