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The Structure of the Class Group of Imaginary Quadratic Fields

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. / Master of Science

Identiferoai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/32572
Date24 May 2005
CreatorsMiller, Nicole Renee
ContributorsMathematics, Parry, Charles J., Haskell, Peter E., Brown, Ezra A.
PublisherVirginia Tech
Source SetsVirginia Tech Theses and Dissertation
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf
RightsIn Copyright, http://rightsstatements.org/vocab/InC/1.0/
RelationNicole.pdf

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