Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-10-31T00:36:31.727Z Has data issue: false hasContentIssue false
  • English
  • Français

NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

Published online by Cambridge University Press:  01 January 2009

YASUHIRO KISHI
YASUHIRO KISHI*
Affiliation:
Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka 811-4192, Japan e-mail: ykishi@fukuoka-edu.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

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.

We prove that the class number of the imaginary quadratic field is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

Keywords

11R1111R29

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 187 - 191
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Ankeny, N. C. and Chowla, S., On the divisibility of the class number of quadratic fields, Pacific J. Math. 5 (1955), 321–324.CrossRefGoogle Scholar
2.Bugeaud, Y. and Shorey, T. N., On the number of solutions of the generalized Ramanujan-Nagell equation, J. Reine Angew. Math. 539 (2001), 55–74.Google Scholar
3.Gross, B. H. and Rohrlich, D. E., Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201–224.CrossRefGoogle Scholar
4.Herschfeld, A., The equation 2x − 3y = d, Bull. Amer. Math. Soc. 42 (1936), 231–234.CrossRefGoogle Scholar
5.Ichimura, H., Note on the class numbers of certain real quadratic fields, Abh. Math. Sem. Univ. Hamburg 73 (2003), 281–288.CrossRefGoogle Scholar
6.Mollin, R. A., Solutions of Diophantine equations and divisibility of class numbers of complex quadratic fields, Glasgow Math. J. 38 (1996), 195–197.CrossRefGoogle Scholar