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

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.

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.

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Leutbecher, Armin. Euclidean fields having a large Lenstra constant. Annales de l'Institut Fourier, Volume 35 (1985) no. 2, pp. 83-106. doi : 10.5802/aif.1011. https://aif.centre-mersenne.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: 84i:12004 | Zbl: 0527.12007

[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: 86d:11091 | Zbl: 0546.12004

[3] S. Lang, Integral points on curves, Publ. IHES, (1960), N° 6. | Numdam | MR: 24 #A86 | Zbl: 0112.13402

[4] H. W. Lenstra Jr., Euclidean number fields of large degree, Invent. Math., 38 (1977), 237-254. | MR: 55 #2836 | Zbl: 0328.12007

[5] H. W. Lenstra Jr., Euclidean number fields, Math. Intelligencer 2, no. 1 (1979), 6-15 ; no. 2 (1980), 73-77, 99-103. | MR: 81m:12001 | Zbl: 0433.12004

[6] A. Leutbecher and J. Martinet, Lenstra's constant and Euclidean number fields, Astérisque, 94 (1982), 87-131. | MR: 85b:11090 | Zbl: 0499.12013

[7] F. J. Van Der Linden, Euclidean rings with two infinite primes, Thesis, Amsterdam, (1984). | Zbl: 0571.12002

[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: 84g:12009 | Zbl: 0491.12005

[9] T. Nagell, Sur un type particulier d'unités algébriques, Ark. Mat., 8 (1969), 163-184. | MR: 42 #3064 | Zbl: 0213.06901

[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: 83g:12009 | Zbl: 0478.12005

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