# On lattice bases with special properties

Ulrich Halbritter; Michael E. Pohst

Journal de théorie des nombres de Bordeaux (2000)

- Volume: 12, Issue: 2, page 437-453
- ISSN: 1246-7405

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topHalbritter, Ulrich, and Pohst, Michael E.. "On lattice bases with special properties." Journal de théorie des nombres de Bordeaux 12.2 (2000): 437-453. <http://eudml.org/doc/248513>.

@article{Halbritter2000,

abstract = {In this paper we introduce multiplicative lattices in $(\mathbb \{R\}^\{>0\})^r$ 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.},

author = {Halbritter, Ulrich, Pohst, Michael E.},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {lattice; units; Shintani zeta function},

language = {eng},

number = {2},

pages = {437-453},

publisher = {Université Bordeaux I},

title = {On lattice bases with special properties},

url = {http://eudml.org/doc/248513},

volume = {12},

year = {2000},

}

TY - JOUR

AU - Halbritter, Ulrich

AU - Pohst, Michael E.

TI - On lattice bases with special properties

JO - Journal de théorie des nombres de Bordeaux

PY - 2000

PB - Université Bordeaux I

VL - 12

IS - 2

SP - 437

EP - 453

AB - In this paper we introduce multiplicative lattices in $(\mathbb {R}^{>0})^r$ 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.

LA - eng

KW - lattice; units; Shintani zeta function

UR - http://eudml.org/doc/248513

ER -

## References

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- [5] M. Pohst, H. Zassenhaus, Algorithmic Algebraic Number Theory. Cambridge University Press1989. Zbl0685.12001MR1033013
- [6] K. Reidemeister, Über die Relativklassenzahl gewisser relativ-quadratischer Zahlkörper. Abh. Math. Sem. Univ. Hamburg1 (1922), 27-48. Zbl48.0171.01JFM48.0171.01
- [7] T. Shintani, On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. Univ. Tokyo IA23 (1976),393-417. Zbl0349.12007MR427231

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