UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Agathocleous, EleniSubject: search.filters.subject.Mathematics

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    Class Numbers of Real Cyclotomic Fields of Conductor pq
    (2009) Agathocleous, Eleni; Washington, Lawrence; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    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.