충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권1호
  • /
  • Pages.169-176
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  • 2010
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

ON THE PARITY OF THE CLASS NUMBER OF SOME REAL BIQUADRATIC FUNCTION FIELD

  • Ahn, Jaehyun (Department of Mathematics Chungnam National University) ;
  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • 투고 : 2009.01.26
  • 심사 : 2010.02.22
  • 발행 : 2010.03.30
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초록

Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. In this paper, we obtain the the criterion for the parity of the ideal class number h(${\mathcal{O}}_K$) of the real biquadratic function field $K=k(\sqrt{P_1},\;\sqrt{P_2})$, where $P_1$, $P_2{\in}{\mathbb{A}}$ be two distinct monic primes of even degree.

키워드

과제정보

연구 과제 주관 기관 : Chungbuk National University

참고문헌

  1. J. Ahn and H. Jung, Kucera group of circular units in function fields. Bull. Korean Math. Soc. 44 (2007), no. 2, 233-239. https://doi.org/10.4134/BKMS.2007.44.2.233
  2. R. Kucera, On the parity of the class number of a biquadratic field. J. Number Theory 52 (1995), no. 1, 43-52. https://doi.org/10.1006/jnth.1995.1054
  3. R. Kucera, On the Stickelberger ideal and circular units of a compositum of quadratic fields. J. Number Theory 56 (1996), no. 1, 139-166. https://doi.org/10.1006/jnth.1996.0008
  4. M. Rosen, Number theory in function fields, Graduate Texts in Mathematics, 210, Springer-Verlag, New York, 2002.