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ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS

Published online by Cambridge University Press:  25 August 2010

YASUHIRO KISHI
YASUHIRO KISHI*
Affiliation:
Department of Mathematics, Fukuoka University of Education, 1-1 Bunkyoumachi Akama, Munakata-shi, Fukuoka 811-4192, Japan e-mail: ykishi@fukuoka-edu.ac.jp
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Abstract

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Let n(≥ 3) be an odd integer. Let k:= $\Q(\sqrt{4-3^n})\)$ be the imaginary quadratic field and k′:= $\Q(\sqrt{-3(4-3^n)})\)$ the real quadratic field. In this paper, we prove that the class number of k is divisible by 3 unconditionally, and the class number of k′ is divisible by 3 if n(≥ 9) is divisible by 3. Moreover, we prove that the 3-rank of the ideal class group of k is at least 2 if n(≥ 9) is divisible by 3.

Keywords

11R1111R29

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010, pp. 575 - 581
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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