On the Euclidean minimum of some real number fields
Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 437-454.

Le but de cet article est de donner des bornes pour le minimum euclidien des corps quadratiques réels et des corps cyclotomiques réels dont le conducteur est une puissance d’un nombre premier.

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.

DOI : 10.5802/jtnb.500
Bayer-Fluckiger, Eva 1 ; Nebe, Gabriele 2

1 Département de Mathématiques EPF Lausanne 1015 Lausanne Switzerland
2 Lehrstuhl D für Mathematik RWTH Aachen 52056 Aachen Germany
@article{JTNB_2005__17_2_437_0,
     author = {Bayer-Fluckiger, Eva and Nebe, Gabriele},
     title = {On the {Euclidean} minimum of some real number fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {437--454},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {2},
     year = {2005},
     doi = {10.5802/jtnb.500},
     zbl = {1161.11032},
     mrnumber = {2211300},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.500/}
}
TY  - JOUR
AU  - Bayer-Fluckiger, Eva
AU  - Nebe, Gabriele
TI  - On the Euclidean minimum of some real number fields
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2005
SP  - 437
EP  - 454
VL  - 17
IS  - 2
PB  - Université Bordeaux 1
UR  - http://www.numdam.org/articles/10.5802/jtnb.500/
DO  - 10.5802/jtnb.500
LA  - en
ID  - JTNB_2005__17_2_437_0
ER  - 
%0 Journal Article
%A Bayer-Fluckiger, Eva
%A Nebe, Gabriele
%T On the Euclidean minimum of some real number fields
%J Journal de théorie des nombres de Bordeaux
%D 2005
%P 437-454
%V 17
%N 2
%I Université Bordeaux 1
%U http://www.numdam.org/articles/10.5802/jtnb.500/
%R 10.5802/jtnb.500
%G en
%F JTNB_2005__17_2_437_0
Bayer-Fluckiger, Eva; Nebe, Gabriele. On the Euclidean minimum of some real number fields. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 437-454. doi : 10.5802/jtnb.500. http://www.numdam.org/articles/10.5802/jtnb.500/

[1] E. Bayer-Fluckiger, Lattices and number fields. Contemp. Math. 241 (1999), 69–84. | MR | Zbl

[2] E. Bayer-Fluckiger, Ideal lattices. A panorama of number theory or the view from Baker’s garden (Zürich, 1999), 168–184, Cambridge Univ. Press, Cambridge, 2002. | Zbl

[3] E. Bayer-Fluckiger, Upper bounds for Euclidean minima. J. Number Theory (to appear). | MR | Zbl

[4] J.W.S. Cassels, An introduction to the geometry of numbers. Springer Grundlehren 99 (1971). | MR | Zbl

[5] J.H. Conway, N.J.A. Sloane, Low Dimensional Lattices VI: Voronoi Reduction of Three-Dimensional Lattices. Proc. Royal Soc. London, Series A 436 (1992), 55–68. | MR | Zbl

[6] J.H. Conway, N.J.A. Sloane, Sphere packings, lattices and groups. Springer Grundlehren 290 (1988). | MR | Zbl

[7] P.M. Gruber, C.G. Lekkerkerker, Geometry of Numbers. North Holland (second edition, 1987) | MR | Zbl

[8] The KANT Database of fields. http://www.math.tu-berlin.de/cgi-bin/kant/database.cgi.

[9] F. Lemmermeyer, The Euclidean algorithm in algebraic number fields. Expo. Math. 13 (1995), 385–416. (updated version available via http://public.csusm.edu/public/FranzL/publ.html). | MR | Zbl

[10] C.T. McMullen, Minkowski’s conjecture, well-rounded lattices and topological dimension., Journal of the American Mathematical Society 18 (3) (2005), 711–734. | Zbl

[11] R. Quême, A computer algorithm for finding new euclidean number fields. J. Théorie de Nombres de Bordeaux 10 (1998), 33–48. | EuDML | Numdam | MR | Zbl

[12] E. Weiss, Algebraic number theory. McGraw-Hill Book Company (1963). | MR | Zbl

[13] M. Dutour, A. Schürmann, F. Vallentin, A Generalization of Voronoi’s Reduction Theory and Applications, (preprint 2005). | Zbl

Cité par Sources :