충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권4호
  • /
  • Pages.625-628
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  • 2010
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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A p-TH ROOT OF A MINKOWSKI UNIT

  • Oh, Jangheon (Department of Applied Mathematics Sejong University)
  • 투고 : 2010.05.10
  • 심사 : 2010.08.12
  • 발행 : 2010.12.30
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초록

The purpose of this paper is to show that there exists a unit whose p-th root generates the first layer of anti-cyclotomic ${\mathbb{Z}}_p$-extension of certain imaginary quadratic number fields.

키워드

참고문헌

  1. H. Cohen, Advanced Topics in Computational Number Theory, Springer, 1999
  2. J. M. Kim and J. Oh, Defining Polynomial of the first layer of anti-cyclotomic $Z_{3}$- extension over imaginary quadratic fields of class number 1, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 3, 18-19. https://doi.org/10.3792/pjaa.80.18
  3. J. Oh, The first layer of $Z^{2}_{2}$ -extension over imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 9, 132-134. https://doi.org/10.3792/pjaa.76.132
  4. J. Oh, On the first layer of anti-cyclotomic $Z_{p}$-extension over imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 3, 19-20. https://doi.org/10.3792/pjaa.83.19
  5. J. Oh, A note on the first layers of $Z_{p}$-extensions, Commun. Korean Math. Soc. 24 (2009), no.3, 1-4. https://doi.org/10.4134/CKMS.2009.24.1.001
  6. J. Oh, Construction of 3-Hilbert class field of certain imaginary quadratic fields, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 1, 18-19. https://doi.org/10.3792/pjaa.86.18
  7. L. Washington, Introduction to Cyclotomic Fields, Graduate Text in Math. 83 (1982), Springer-Verlag