Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CONSTRUCTION OF THE HILBERT CLASS FIELD OF SOME IMAGINARY QUADRATIC FIELDS

  • Oh, Jangheon (Faculty of Mathematics and Statistics Sejong University)
  • Received : 2018.03.08
  • Accepted : 2018.06.07
  • Published : 2018.06.30
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Abstract

In the paper [4], we constructed 3-part of the Hilbert class field of imaginary quadratic fields whose class number is divisible exactly by 3. In this paper, we extend the result for any odd prime p.

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References

  1. H.Cohen, Advanced Topics in Computational Number Theory, Springer, 1999.
  2. J.Minardi, Iwasawa modules for $\mathbb{Z}_p^d$-extensions of algebraic number fields, Ph.D dissertation, University of Washington, 1986.
  3. J.Oh, On the first layer of anti-cyclotomic $\mathbb{Z}_p$-extension of imaginary quadratic fields, Proc. of The Japan Acad. Ser.A 83 (2007) (3),19-20. https://doi.org/10.3792/pjaa.83.19
  4. J.Oh, Construction of 3-Hilbert class field of certain imaginary quadratic fields, Proc. of The Japan Acad. Ser.A 86 (2010) (1), 18-19. https://doi.org/10.3792/pjaa.86.18
  5. L.Washington, Introduction to cyclotomic fields, Springer, New York, 1982.