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http://dx.doi.org/10.14403/jcms.2012.25.1.091

ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD  

Oh, Jangheon (Department of Applied Mathematics Sejong University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.1, 2012 , pp. 91-95 More about this Journal
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 ${\mathbb{{Q}}}({\sqrt{3d}})$.
Keywords
Hilbert class field; anti-cyclotomic extension; Kummer extension;
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Times Cited By KSCI : 1  (Citation Analysis)
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