On lattice bases with special properties
Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 437-453.

In this paper we introduce multiplicative lattices in ( >0 ) r and determine finite unions of suitable simplices as fundamental domains for sublattices of finite index. For this we define cyclic non-negative bases in arbitrary lattices. These bases are then used to calculate Shintani cones in totally real algebraic number fields. We mainly concentrate our considerations to lattices in two and three dimensions corresponding to cubic and quartic fields.

Nous introduisons ici des réseaux multiplicatifs de ( >0 ) r et déterminons des réunions finies de simplexes convenables comme domaines fondamentaux de sous-réseaux d’indices finis. Nous définissons pour cela des bases cycliques positives de réseaux arbitraires. Nous utilisons ces bases pour calculer les cônes de Shintani dans des corps totalement réels de nombres algébriques. Nous nous intéressons plus particulierement aux réseaux en dimensions deux et trois correspondants à des corps cubiques ou quartiques.

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Ulrich Halbritter; Michael E. Pohst. On lattice bases with special properties. Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 2, pp. 437-453. doi : 10.5802/jtnb.289. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.289/

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