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REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS

Published online by Cambridge University Press:  21 March 2011

AKIKO ITO
AKIKO ITO*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan e-mail: m07004a@math.nagoya-u.ac.jp
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Abstract

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We consider the divisibility of the class numbers of imaginary quadratic fields , where q is an odd prime number, k and n are positive integers. Suppose that k ≡ 1 mod 2 or n ≢ 3 mod 6. We show that the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 3 mod 8. This is a generalization of the result of Kishi for imaginary quadratic fields when k ≡ 1 mod 2 or n ≢ 3 mod 6. We also show that the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 1 mod 4 and the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 7 mod 8.

Keywords

11R1111R29
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 379 - 389
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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