Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-18T06:55:45.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Units and Class Numbers of Real Quadratic Fields

Published online by Cambridge University Press:  22 January 2016

Hideo Yokoi
Hideo Yokoi*
Affiliation:
Mathematical Institute, Nagoya University
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.

The aim of this paper is to prove the following main theorem:

THEOREM. For the discriminant d>0 of a real quadratic field let (x,y) = (t,u) be the least positive integral solution of Pell’s equation x2 — dy2 = 4 and put and denote by hd the ideal class number.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 61 - 65
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Baker, A., Linear forms in the logarithmus of algebraic numbers, I, II, III. Mathematika 13 (1966), 204–216, 14 (1967), 102–107, 202–228.Google Scholar
[2] Hua, L.K., On the least solution of Pell’s equation. Bull. Amer. Math. Soc. 48 (1942), 731–735.CrossRefGoogle Scholar
[3] Landau, E., Vorlesungen über Zahlentheorie. Chelsea, New York, 1946.Google Scholar
[4] Newman, M., Bounds for class numbers. Proc. Sympo. pure Math. VIII (1965), 70–77.CrossRefGoogle Scholar
[5] Stark, H.M., A complete determination of the complex quadratic fields of class number one. Michigan Math. J. 14 (1967), 1–27.CrossRefGoogle Scholar