Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD

  • Oh, Jangheon (Department of Applied Mathematics Sejong University)
  • Published : 2012.02.15
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Abstract

In this paper, we show how to construct the first layer $k^{\alpha}_{1}$ of anti-cyclotomic ${\mathbb{{Z}}}_{3}$-extension of imaginary quadratic fields $k(=\;{\mathbb{{Q}}}(\sqrt{-d}))$ when the Sylow subgroup of class group of k is 3-elementary, and give an example. This example is different from the one we obtained before in the sense that when we write $k^{\alpha}_{1}\;=\;k({\eta}),{\eta}$ is obtained from non-units of ${\mathbb{{Q}}}({\sqrt{3d}})$.

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References

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Cited by

  1. CONSTRUCTION OF THE FIRST LAYER OF ANTI-CYCLOTOMIC EXTENSION vol.21, pp.3, 2013, https://doi.org/10.11568/kjm.2013.21.3.265
  2. ON THE ANTICYCLOTOMIC ℤp-EXTENSION OF AN IMAGINARY QUADRATIC FIELD vol.23, pp.3, 2015, https://doi.org/10.11568/kjm.2015.23.3.323