Regulator and Class Group Tabulation in Real Quadratic Number Fields

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dc.contributor.advisorJacobson, Michael John Jr.
dc.contributor.authorDocherty, Austin George
dc.contributor.committeememberScheidler, Renate
dc.contributor.committeememberNguyen, Dang Khoa
dc.date2025-11
dc.date.accessioned2025-07-03T21:27:23Z
dc.date.available2025-07-03T21:27:23Z
dc.date.issued2025-06-11
dc.description.abstractIn this work, the regulator R_∆ and class group structure Cl_∆ for all real quadratic fields Q(√∆), ∆ ≤ 1.1 × 2^(40) are computed conditionally. The results are then verified unconditionally correct for ∆ ≤ 1.1 × 10^(12) (that is, ∆ ≤ 2^(40)). This is achieved, in part, by adapting previous methods for computation in imaginary quadratic fields and proving certain time complexity results on them. A statistical aggregate on the tabulated results is made and compared to several longstanding conjectures and conditional theorems. Several fields are also found and documented to have invariants with novel properties and class group structures.
dc.identifier.citationDocherty, A. (2025). Regulator and class group tabulation in real quadratic number fields (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.urihttps://hdl.handle.net/1880/122163
dc.language.isoenen
dc.publisher.facultyScience
dc.rightsUnless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en
dc.subjectNumber Theory
dc.subjectReal Quadratic Fields
dc.subjectRegulator
dc.subjectClass Group
dc.subject.classificationComputer Science
dc.subject.classificationEducation--Mathematics
dc.titleRegulator and Class Group Tabulation in Real Quadratic Number Fields
dc.typemaster thesis
thesis.degree.disciplineComputer Science
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.thesis.accesssetbystudentI do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.

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