Hermite constant and Voronoï theory over a quaternion skew field

Coulangeon, Renaud; Watanabe, Takao

Osaka J. Math., Tome 43 (2006) no. 2, p. 517-556 / Harvested from Project Euclid

Résumé

The Hermite constant $\gamma_n(D)$ of a quaternion skew field $D$ over a global field is defined and studied. We obtain an upper bound of $\gamma_{n}(D)$. In the case that the base field is a number field, we introduce the notion of quaternionic Humbert forms over $D$. Then $\gamma_{n}(D)$ is characterized as a critical value of the Hermite invariants for $n$-ary quaternionic Humbert forms. We extend Voronoï's theorem on extreme forms to quaternionic Humbert forms.

Publié le : 2006-09-14
Classification: 11H50, 11H55, 11R52

@article{1159190000,
     author = {Coulangeon, Renaud and Watanabe, Takao},
     title = {Hermite constant and Vorono\"\i\ theory over a quaternion skew field},
     journal = {Osaka J. Math.},
     volume = {43},
     number = {2},
     year = {2006},
     pages = { 517-556},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1159190000}
}

Coulangeon, Renaud; Watanabe, Takao. Hermite constant and Voronoï theory over a quaternion skew field. Osaka J. Math., Tome 43 (2006) no. 2, pp.  517-556. http://gdmltest.u-ga.fr/item/1159190000/