The Structure of the Class Group of Imaginary Quadratic Fields
dc.contributor.author | Miller, Nicole Renee | en |
dc.contributor.committeechair | Parry, Charles J. | en |
dc.contributor.committeemember | Haskell, Peter E. | en |
dc.contributor.committeemember | Brown, Ezra A. | en |
dc.contributor.department | Mathematics | en |
dc.date.accessioned | 2014-03-14T20:36:17Z | en |
dc.date.adate | 2005-05-24 | en |
dc.date.available | 2014-03-14T20:36:17Z | en |
dc.date.issued | 2005-05-11 | en |
dc.date.rdate | 2008-05-24 | en |
dc.date.sdate | 2005-05-11 | en |
dc.description.abstract | Let Q(√(-d)) be an imaginary quadratic field with discriminant Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with cyclic factors that have order a large power of 2, or fields with class groups of high 5-ranks or high 7-ranks. | en |
dc.description.degree | Master of Science | en |
dc.identifier.other | etd-05112005-124308 | en |
dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-05112005-124308/ | en |
dc.identifier.uri | http://hdl.handle.net/10919/32572 | en |
dc.publisher | Virginia Tech | en |
dc.relation.haspart | Nicole.pdf | en |
dc.rights | In Copyright | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject | 7-rank | en |
dc.subject | 5-rank | en |
dc.subject | Positive Definite Forms | en |
dc.subject | Genera | en |
dc.subject | Class Group | en |
dc.subject | Binary Quadratic Fields | en |
dc.title | The Structure of the Class Group of Imaginary Quadratic Fields | en |
dc.type | Thesis | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
thesis.degree.level | masters | en |
thesis.degree.name | Master of Science | en |
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