Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-16T17:02:31.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Minorations d’unités fondamentales—applications

Published online by Cambridge University Press:  22 January 2016

Stéphane Louboutin
Stéphane Louboutin*
Affiliation:
Université de Caen, U. F. R. Sciences, Département de Mathématiques, Esplanade de la Paix, 14032 Caen Cedex, France email: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Un idéal entier I d’un corps quadratique réel k est dit primitif lorsque n ∈ N* et (n) divise I impliquent n = 1. Un idéal entier est primitif si et seulement si il vérifie les trois conditions suivantes:

(i) il n’est divisible par aucun idéal premier inerte,

(ii) il n’est divisible par le carré d’aucun idéal premier ramifié,

(iii) si il est divisible par un idéal premier totalement décomposé, alors il n’est pas divisible par son idéal premier conjugué.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 130 , June 1993 , pp. 1 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

Bibliographie

[1] Amara, H., Groupe des classes et unité fondamentale des extensions quadratiques relatives à un corps quadratique imaginaire principal, Pacific J. Math., 96 (1981), 1–12.Google Scholar
[2] Azuhata, T., On the fundamental units and the class numbers of real quadratic fields, Proc. Japan Acad., Sci. 62 (1986), 97–100.Google Scholar
[3] Bernstein, L., Fundamental unit and cycles in the period of real quadratic number fields, Pacific J. Math., 63 (1976), 37–78.CrossRefGoogle Scholar
[4] Dubois, E. and Levesque, C., On determining certain real quadratic fields with class number one and relating this property to continued fractions and primality properties, Nagoya Math. J., 124 (1991), 157–180.CrossRefGoogle Scholar
[5] Levesque, C. et Rhin, G., Two families of periodic Jacobi algorithms with period lengths going to infinity, J. Number Theory., 37 (1991), 173–180.CrossRefGoogle Scholar
[6] Louboutin, S., Prime producing quadratic polynomials andclass-numbers of real quadratic fields, Canad. J. Math., 42 (1990), 315–341.Google Scholar
[7] Williams, H. C., Continued fractions and number-theoretic computations, Rocky Mountain J. Math., 15 (1985), 621–655.Google Scholar
[8] Williams, H. C., The period length of Voronoi’s algorithm for certain cubic orders, Publicationes Math. Debrecen., 37 (1990), 245–265.CrossRefGoogle Scholar
[9] Yamamoto, Y., Real quadratic number fields with large fundamental units, Osaka J. Math., 8(1971), 261–270.Google Scholar