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Investigations of Highly Irregular Primes and Associated Ray Class Fields

dc.contributor.advisorWashington, Lawrenceen_US
dc.contributor.authorStern, Morgan Benjaminen_US
dc.description.abstractWe investigate properties of the class number of certain ray class fields of prime conductor lying above imaginary quadratic fields. While most previous work in this area restricted to the case of imaginary quadratic fields of class number 1, we deal almost exclusively with class number 2. Our main results include finding 5 counterexamples to a generalization of the famous conjecture of Vandiver that the class number of the pth real cyclotomic field is never divisible by p. We give these counterexamples the name highly irregular primes due to the fact that any counterexample of classical Vandiver is an irregular prime. In addition we explore whether several consequences of Vandiver's conjecture still hold for these highly irregular primes, including the cyclicity of certain class groups.en_US
dc.titleInvestigations of Highly Irregular Primes and Associated Ray Class Fieldsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.subject.pqcontrolledTheoretical mathematicsen_US
dc.subject.pquncontrolledclass numberen_US
dc.subject.pquncontrolledhighly irregular primeen_US
dc.subject.pquncontrolledray class fielden_US
dc.subject.pquncontrolledVandivers conjectureen_US

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