ANTI-CYCLOTOMIC EXTENSION AND HILBERT CLASS FIELD

Abstract

In this paper, we show how to construct the first layer ka 1 of anti-cyclotomic Z3-extension of imaginary quadratic fields k(= Q( −d)) when the Sylow subgroup of class group of k is 3elementary, and give an example. This example is different from the one we obtained before in the sense that when we write ka 1 = k(η), η is obtained from non-units of Q(

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