Computing non-square elements of square norm in a number field.

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dc.contributor.authorKent, Joe
dc.date.accessioned2024-04-10T22:37:18Z
dc.date.available2024-04-10T22:37:18Z
dc.date.issued2023
dc.description.abstractIn this thesis we explore the unit group of the ring of integers of number fields. In our exploration we look at Dirichlet’s unit theorem which shows that the unit group is a finitely generated abelian group. This will allow us to explore computing the generating set of the unit group. From this basis we then extend the computation of unit groups to describe and implement an algorithm in PARI for finding elements in the kernel of the norm mapping K×/K×2 Q×/Q×2. Elements in this mapping are of particular interest for finding Brauer Manin obstructions with current implementations using a set of fundamental units.
dc.identifier.urihttps://hdl.handle.net/10092/106893
dc.identifier.urihttps://doi.org/10.26021/15279
dc.languageEnglish
dc.language.isoen
dc.rightsAll Right Reserved
dc.rights.urihttps://canterbury.libguides.com/rights/theses
dc.titleComputing non-square elements of square norm in a number field.
dc.typeTheses / Dissertations
thesis.degree.grantorUniversity of Canterbury
thesis.degree.levelMasters
thesis.degree.nameMaster of Engineering
uc.collegeFaculty of Engineering
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