Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A REMARK OF SOME IMAGINARY QUADRATIC FIELDS WITH ODD CLASS NUMBERS

  • Kim, Hyun (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Lee, Keumyeon (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Cheong, Cheoljo (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Park, Hwasin (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • Received : 2013.12.23
  • Accepted : 2014.01.03
  • Published : 2014.03.25
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Abstract

Let D be a square-free positive integer and let $K_D=\mathbb{Q}(\sqrt{-D})$ be the imaginary quadratic field. And let $h_D$ be the class number of the number field $K_D$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $l{\equiv}3$ (mod 4), then $h_D$ is odd.

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References

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