Euclidean fields having a large Lenstra constant
Annales de l'Institut Fourier, Tome 35 (1985) no. 2, pp. 83-106.

Fondée sur une méthode de H. W. Lenstra Jr., cette note représente 143 exemples nouveaux des corps de nombres euclidiens. Il s’agit des corps de degré n=7,8,9 et 10 et de rang des unités ≤5. La recherche de ces exemples a révélé aussi quelques corps de discriminant petit, comparé avec la borne inférieure d’Odlyzko.

Based on a method of H. W. Lenstra Jr. in this note 143 new Euclidean number fields are given of degree n=7,8,9 and 10 and of unit rank ≤5. The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.

@article{AIF_1985__35_2_83_0,
     author = {Leutbecher, Armin},
     title = {Euclidean fields having a large {Lenstra} constant},
     journal = {Annales de l'Institut Fourier},
     pages = {83--106},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {35},
     number = {2},
     year = {1985},
     doi = {10.5802/aif.1011},
     mrnumber = {86j:11107},
     zbl = {0546.12005},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1011/}
}
TY  - JOUR
AU  - Leutbecher, Armin
TI  - Euclidean fields having a large Lenstra constant
JO  - Annales de l'Institut Fourier
PY  - 1985
SP  - 83
EP  - 106
VL  - 35
IS  - 2
PB  - Institut Fourier
PP  - Grenoble
UR  - https://www.numdam.org/articles/10.5802/aif.1011/
DO  - 10.5802/aif.1011
LA  - en
ID  - AIF_1985__35_2_83_0
ER  - 
%0 Journal Article
%A Leutbecher, Armin
%T Euclidean fields having a large Lenstra constant
%J Annales de l'Institut Fourier
%D 1985
%P 83-106
%V 35
%N 2
%I Institut Fourier
%C Grenoble
%U https://www.numdam.org/articles/10.5802/aif.1011/
%R 10.5802/aif.1011
%G en
%F AIF_1985__35_2_83_0
Leutbecher, Armin. Euclidean fields having a large Lenstra constant. Annales de l'Institut Fourier, Tome 35 (1985) no. 2, pp. 83-106. doi : 10.5802/aif.1011. https://www.numdam.org/articles/10.5802/aif.1011/

[1] F. Diaz Y Diaz, Valeurs minima du discriminant des corps de degré 7 ayant une seule place réelle, C.R.A.S., Paris, 296 (1983), 137-139. | MR | Zbl

[2] F. Diaz Y Diaz, Valeurs minima du discriminant pour certains types de corps de degré 7, Ann. de l'Inst. Fourier, 34-3 (1984), 29-38. | Numdam | MR | Zbl

[3] S. Lang, Integral points on curves, Publ. IHES, (1960), N° 6. | Numdam | MR | Zbl

[4] H. W. Lenstra Jr., Euclidean number fields of large degree, Invent. Math., 38 (1977), 237-254. | MR | Zbl

[5] H. W. Lenstra Jr., Euclidean number fields, Math. Intelligencer 2, no. 1 (1979), 6-15 ; no. 2 (1980), 73-77, 99-103. | MR | Zbl

[6] A. Leutbecher and J. Martinet, Lenstra's constant and Euclidean number fields, Astérisque, 94 (1982), 87-131. | Numdam | MR | Zbl

[7] F. J. Van Der Linden, Euclidean rings with two infinite primes, Thesis, Amsterdam, (1984). | Zbl

[8] J. Martinet, Petits discriminants des corps de nombre, J. V. Armitage (éd.), Journées Arithmétiques 1980, Cambridge University Press. LMS Lecture Notes séries, 56 (1982), 151-193. | MR | Zbl

[9] T. Nagell, Sur un type particulier d'unités algébriques, Ark. Mat., 8 (1969), 163-184. | MR | Zbl

[10] M. Pohst, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. of Number Th., 14 (1982), 99-117. | MR | Zbl

  • Foster, Kurt HT90 and “simplest” number fields, Illinois Journal of Mathematics, Volume 55 (2011) no. 4 | DOI:10.1215/ijm/1373636699
  • Mulay, S.B. Polynomial-mappings and M-equivalence, Journal of Algebra, Volume 302 (2006) no. 2, p. 862 | DOI:10.1016/j.jalgebra.2006.04.027
  • Cohen, Henri Appendix C: Tables, Advanced Topics in Computional Number Theory, Volume 193 (2000), p. 533 | DOI:10.1007/978-1-4419-8489-0_12
  • Selmane, Schehrazad Non-primitive number fields of degree eight and of signature (2,3), (4,2), and (6,1) with small discriminant, Mathematics of Computation, Volume 68 (1999) no. 225, p. 333 | DOI:10.1090/s0025-5718-99-00998-9
  • Cohen, H.; y Diaz, F.; Olivier, M. Computing ray class groups, conductors and discriminants, Mathematics of Computation, Volume 67 (1998) no. 222, p. 773 | DOI:10.1090/s0025-5718-98-00912-0
  • Cohen, H.; Diaz, F. Diaz; Olivier, M. Computing ray class groups, conductors and discriminants, Algorithmic Number Theory, Volume 1122 (1996), p. 49 | DOI:10.1007/3-540-61581-4_40
  • Schulze, Volker Verallgemeinerte Euklidische Algorithmen, Archiv der Mathematik, Volume 64 (1995) no. 4, p. 313 | DOI:10.1007/bf01198085
  • Diaz y Diaz, F.; Olivier, M. Imprimitive ninth-degree number fields with small discriminants, Mathematics of Computation, Volume 64 (1995) no. 209, p. 305 | DOI:10.1090/s0025-5718-1995-1260128-x
  • Desmedt, Yvo G.; Frankel, Yair Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group, SIAM Journal on Discrete Mathematics, Volume 7 (1994) no. 4, p. 667 | DOI:10.1137/s0895480192224713
  • Bergé, A.-M.; Martinet, J.; Olivier, M. The computation of sextic fields with a quadratic subfield, Mathematics of Computation, Volume 54 (1990) no. 190, p. 869 | DOI:10.1090/s0025-5718-1990-1011438-8
  • Leutbecher, Armin; Niklasch, Gerhard On cliques of exceptional units and Lenstra's construction of Euclidean fields, Number Theory, Volume 1380 (1989), p. 150 | DOI:10.1007/bfb0086551

Cité par 11 documents. Sources : Crossref