Euclidean fields having a large Lenstra constant

Armin Leutbecher

Annales de l'institut Fourier (1985)

  • Volume: 35, Issue: 2, page 83-106
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Leutbecher, Armin. "Euclidean fields having a large Lenstra constant." Annales de l'institut Fourier 35.2 (1985): 83-106. <http://eudml.org/doc/74679>.

@article{Leutbecher1985,
abstract = {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 $\le 5$. The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.},
author = {Leutbecher, Armin},
journal = {Annales de l'institut Fourier},
keywords = {Lenstra constant; Euclidean number fields; degree and 10; unit rank; small discriminant; lower bounds of Odlyzko},
language = {eng},
number = {2},
pages = {83-106},
publisher = {Association des Annales de l'Institut Fourier},
title = {Euclidean fields having a large Lenstra constant},
url = {http://eudml.org/doc/74679},
volume = {35},
year = {1985},
}

TY - JOUR
AU - Leutbecher, Armin
TI - Euclidean fields having a large Lenstra constant
JO - Annales de l'institut Fourier
PY - 1985
PB - Association des Annales de l'Institut Fourier
VL - 35
IS - 2
SP - 83
EP - 106
AB - 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 $\le 5$. The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.
LA - eng
KW - Lenstra constant; Euclidean number fields; degree and 10; unit rank; small discriminant; lower bounds of Odlyzko
UR - http://eudml.org/doc/74679
ER -

References

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  1. [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. Zbl0527.12007MR84i:12004
  2. [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. Zbl0546.12004MR86d:11091
  3. [3] S. LANG, Integral points on curves, Publ. IHES, (1960), N° 6. Zbl0112.13402MR24 #A86
  4. [4] H. W. LENSTRA jr., Euclidean number fields of large degree, Invent. Math., 38 (1977), 237-254. Zbl0328.12007MR55 #2836
  5. [5] H. W. LENSTRA jr., Euclidean number fields, Math. Intelligencer 2, no. 1 (1979), 6-15 ; no. 2 (1980), 73-77, 99-103. Zbl0433.12004MR81m:12001
  6. [6] A. LEUTBECHER and J. MARTINET, Lenstra's constant and Euclidean number fields, Astérisque, 94 (1982), 87-131. Zbl0499.12013MR85b:11090
  7. [7] F. J. van der LINDEN, Euclidean rings with two infinite primes, Thesis, Amsterdam, (1984). Zbl0571.12002
  8. [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. Zbl0491.12005MR84g:12009
  9. [9] T. NAGELL, Sur un type particulier d'unités algébriques, Ark. Mat., 8 (1969), 163-184. Zbl0213.06901MR42 #3064
  10. [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. Zbl0478.12005MR83g:12009

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