Class Numbers of Real Cyclotomic Fields of Conductor pq

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dc.contributor.advisorWashington, Lawrenceen_US
dc.contributor.authorAgathocleous, Elenien_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2010-02-19T06:36:44Z
dc.date.available2010-02-19T06:36:44Z
dc.date.issued2009en_US
dc.description.abstract<italic>The class numbers h+ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows and that is why other methods have been developed, which approach the problem from different angles. In this thesis we extend a method of Schoof that was designed for real cyclotomic fields of prime conductor to real cyclotomic fields of conductor equal to the product of two distinct odd primes. Our method calculates the index of a specific group of cyclotomic units in the full group of units of the field. This index has h+ as a factor. We then remove from the index the extra factor that does not come from h+ and so we have the order of h+. We apply our method to real cyclotomic fields of conductor < 2000 and we test the divisibility of h+ by all primes < 10000. Finally, we calculate the full order of the l-part of h+ for all odd primes l < 10000.</italic>en_US
dc.identifier.urihttp://hdl.handle.net/1903/9832
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledclassen_US
dc.subject.pquncontrolledcyclotomicen_US
dc.subject.pquncontrolledfieldsen_US
dc.subject.pquncontrollednumberen_US
dc.titleClass Numbers of Real Cyclotomic Fields of Conductor pqen_US
dc.typeDissertationen_US

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