The development of the principal genus theorem

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dc.citation.epage561en_US
dc.citation.spage529en_US
dc.contributor.authorLemmermeyer, Franzen_US
dc.contributor.editorGoldstein, C.
dc.contributor.editorSchappacher, N.
dc.contributor.editorSchwermer, J.
dc.date.accessioned2019-04-25T10:59:21Z
dc.date.available2019-04-25T10:59:21Z
dc.date.issued2007en_US
dc.departmentDepartment of Mathematicsen_US
dc.descriptionChapter VIII.3
dc.description.abstractGenus theory today belongs to algebraic number theory and deals with a certain part of the ideal class group of a number field that is more easily accessible than the rest. Historically, the importance of genus theory stems from the fact that it was the essential algebraic ingredient in the derivation of the classical reciprocity laws, from Gauss’s second proof, via Kummer’s contributions, all the way to Takagi’s reciprocity law for p-th power residues.en_US
dc.identifier.doi10.1007/978-3-540-34720-0_20en_US
dc.identifier.doi10.1007/978-3-540-34720-0en_US
dc.identifier.eisbn9783540347200
dc.identifier.isbn9783540204411
dc.identifier.urihttp://hdl.handle.net/11693/50940
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.ispartofThe shaping of arithmetic after C. F. Gauss’s disquisitiones arithmeticaeen_US
dc.relation.isversionofhttps://doi.org/10.1007/978-3-540-34720-0_20en_US
dc.relation.isversionofhttps://doi.org/10.1007/978-3-540-34720-0en_US
dc.subjectGalois groupen_US
dc.subjectQuadratic numberen_US
dc.subjectCyclic extensionen_US
dc.subjectAlgebraic number theoryen_US
dc.subjectBinary quadratic formen_US
dc.titleThe development of the principal genus theoremen_US
dc.typeBook Chapteren_US

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