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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- [4] R. Okazaki, An elementary proof for a theorem of Thomas and Vasquez. J. Number Th.55 (1995), 197-208. Zbl0853.11087MR1366570
- [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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