Binary quadratic forms and ray class groups

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dc.contributor.authorEum, Ick Sunko
dc.contributor.authorKoo, Ja Kyungko
dc.contributor.authorShin, Dong Hwako
dc.date.accessioned2020-04-28T09:20:08Z-
dc.date.available2020-04-28T09:20:08Z-
dc.date.created2018-08-06-
dc.date.created2018-08-06-
dc.date.created2018-08-06-
dc.date.issued2020-04-
dc.identifier.citationPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, v.150, no.2, pp.695 - 720-
dc.identifier.issn0308-2105-
dc.identifier.urihttp://hdl.handle.net/10203/274031-
dc.description.abstractLet K be an imaginary quadratic field different from $\open{Q}(\sqrt {-1})$ and $\open{Q}(\sqrt {-3})$. For a positive integer N, let K-N be the ray class field of K modulo $N {\cal O}_K$. By using the congruence subgroup +/- Gamma(1)(N) of SL2(DOUBLE-STRUCK CAPITAL Z), we construct an extended form class group whose operation is basically the Dirichlet composition, and explicitly show that this group is isomorphic to the Galois group Gal(K-N/K). We also present an algorithm to find all distinct form classes and show how to multiply two form classes. As an application, we describe Gal(K-N(ab)/K) in terms of these extended form class groups for which K-N(ab) is the maximal abelian extension of K unramified outside prime ideals dividing NOK.-
dc.languageEnglish-
dc.publisherCAMBRIDGE UNIV PRESS-
dc.titleBinary quadratic forms and ray class groups-
dc.typeArticle-
dc.identifier.wosid000524939000006-
dc.identifier.scopusid2-s2.0-85060380850-
dc.type.rimsART-
dc.citation.volume150-
dc.citation.issue2-
dc.citation.beginningpage695-
dc.citation.endingpage720-
dc.citation.publicationnamePROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS-
dc.identifier.doi10.1017/prm.2018.163-
dc.contributor.localauthorKoo, Ja Kyung-
dc.contributor.nonIdAuthorEum, Ick Sun-
dc.contributor.nonIdAuthorShin, Dong Hwa-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorBinary quadratic forms-
dc.subject.keywordAuthorclass field theory-
dc.subject.keywordAuthorclass groups-
dc.subject.keywordAuthorcomplex multiplication-
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