호남수학학술지 (Honam Mathematical Journal)

  • 제36권1호
  • /
  • Pages.147-155
  • /
  • 2014
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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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)
  • 투고 : 2013.12.23
  • 심사 : 2014.01.03
  • 발행 : 2014.03.25
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초록

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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참고문헌

  1. Z. I. Borevich and I. R. Shafarevich, Number Theory, New York, 1966.
  2. H. Cohn, Advanced number theory, New York, Dover, 1980.
  3. L. E. Dickson, Introduction to the Theory of Numbers, New York, Dover, 1957.
  4. J. Oesterla, Nombres de classes des corps quadratiques imaginaries, Asttrique (1985), 121-122, 309-323.
  5. P. Ribenboim, Algebraic Numbers, John Wiley and Sons, Inc, 1972.