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A REMARK OF SOME IMAGINARY QUADRATIC FIELDS WITH ODD CLASS NUMBERS

  • Received : 2013.12.23
  • Accepted : 2014.01.03
  • Published : 2014.03.25

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.

Keywords

class number

References

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