On some arithmetic properties of Siegel functions (II)

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dc.contributor.authorJung, Ho Yunko
dc.contributor.authorKoo, JaKyungko
dc.contributor.authorShin, Dong Hwako
dc.date.accessioned2014-08-28-
dc.date.available2014-08-28-
dc.date.created2013-07-22-
dc.date.created2013-07-22-
dc.date.issued2014-01-
dc.identifier.citationFORUM MATHEMATICUM, v.26, no.1, pp.25 - 57-
dc.identifier.issn0933-7741-
dc.identifier.urihttp://hdl.handle.net/10203/187426-
dc.description.abstractLet 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.-
dc.languageEnglish-
dc.publisherWALTER DE GRUYTER GMBH-
dc.subjectGALOIS MODULE STRUCTURE-
dc.subjectELLIPTIC FUNCTIONS-
dc.subjectNORMAL BASES-
dc.subjectCLASS FIELDS-
dc.subjectNUMBER-FIELDS-
dc.subjectCONJECTURE-
dc.subjectINVARIANTS-
dc.titleOn some arithmetic properties of Siegel functions (II)-
dc.typeArticle-
dc.identifier.wosid000329207000002-
dc.identifier.scopusid2-s2.0-84925444785-
dc.type.rimsART-
dc.citation.volume26-
dc.citation.issue1-
dc.citation.beginningpage25-
dc.citation.endingpage57-
dc.citation.publicationnameFORUM MATHEMATICUM-
dc.identifier.doi10.1515/FORM.2011.148-
dc.contributor.localauthorKoo, JaKyung-
dc.contributor.nonIdAuthorJung, Ho Yun-
dc.contributor.nonIdAuthorShin, Dong Hwa-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorClass fields-
dc.subject.keywordAuthormodular forms and functions-
dc.subject.keywordAuthornormal bases-
dc.subject.keywordAuthornormal p-integral bases-
dc.subject.keywordAuthorSiegel functions-
dc.subject.keywordPlusGALOIS MODULE STRUCTURE-
dc.subject.keywordPlusELLIPTIC FUNCTIONS-
dc.subject.keywordPlusNORMAL BASES-
dc.subject.keywordPlusCLASS FIELDS-
dc.subject.keywordPlusNUMBER-FIELDS-
dc.subject.keywordPlusCONJECTURE-
dc.subject.keywordPlusINVARIANTS-
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