On some arithmetic properties of Siegel functions (II)

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Let K be an imaginary quadratic field of discriminant d(K) <= -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(m))2/K-(pm) for a prime p >= 5 and a positive integer m relatively prime to p and then find normal bases of all intermediate fields over K-(pm) by utilizing Kawamoto's arguments. We further investigate certain Galois module structure of the field extension K-(p(m))n/K-(p(m))l with n >= 2l, which would be an extension of Komatsu's work.
Publisher
WALTER DE GRUYTER GMBH
Issue Date
2014-01
Language
English
Article Type
Article
Keywords

GALOIS MODULE STRUCTURE; ELLIPTIC FUNCTIONS; NORMAL BASES; CLASS FIELDS; NUMBER-FIELDS; CONJECTURE; INVARIANTS

Citation

FORUM MATHEMATICUM, v.26, no.1, pp.25 - 57

ISSN
0933-7741
DOI
10.1515/FORM.2011.148
URI
http://hdl.handle.net/10203/187426
Appears in Collection
MA-Journal Papers(저널논문)
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