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On lattice bases with special properties

Ulrich HalbritterMichael E. Pohst — 2000

Journal de théorie des nombres de Bordeaux

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.

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