On humbert-minkowski's constant for a number field
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. ©1997 American Mathematical Society.
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Proceedings of the American Mathematical Society, Volumen 125, Issue 11, 2018, Pages 3195-3202
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