• Korean Journal of Mathematics
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• v.21 no.3
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• pp.265-270
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• 2013

In this paper, using a theorem of Brink for prime decomposition of the anti-cyclotomic extension, we explicitly construct the first layer of the anti-cyclotomic $\mathbb{Z}_3$-extension of imaginary quadratic fields.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.91-95
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• 2012

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 ${\mathbb{{Q}}}({\sqrt{3d}})$.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.1-4
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• 2009

In this paper we explicitly compute a Minkowski unit of a real abelian field and give a criterion when the first layer of anti-cyclotomic ${\mathbb{Z}}_3$-extension of an imaginary quadratic field is unramified everywhere.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.625-628
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• 2010

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.