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On lattice bases with special properties

Ulrich Halbritter, Michael 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.

On metacyclic extensions

Masanari Kida (2012)

Journal de Théorie des Nombres de Bordeaux

Galois extensions with various metacyclic Galois groups are constructed by means of a Kummer theory arising from an isogeny of certain algebraic tori. In particular, our method enables us to construct algebraic tori parameterizing metacyclic extensions.

On Minkowski units constructed by special values of Siegel modular functions

Takashi Fukuda, Keiichi Komatsu (2003)

Journal de théorie des nombres de Bordeaux

Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field k 6 of ( e x p ( 2 π i / 5 ) ) modulo 6 . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group G ( k 6 / ) for the special values. Futhermore we construct the full unit group of k 6 using modular and circular units under the GRH.

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny (2010)

RAIRO - Theoretical Informatics and Applications

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

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