2014
DOI: 10.1515/form.2011.148
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On some arithmetic properties of Siegel functions (II)

Abstract: Let K be an imaginary quadratic field of discriminant d K Ä 7. We deal with problems of constructing normal bases between abelian extensions of K by making use of singular values of Siegel functions. First, we find normal bases of ring class fields of orders of bounded conductors depending on d K over K by using a criterion deduced from the Frobenius determinant relation. Next, denoting by K .N / the ray class field modulo N of K for an integer N 2 we consider the field extension K .p 2 m/ =K .pm/ for a prime … Show more

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