Let K be an imaginary quadratic field with class number one and let [Special characters omitted.] be a degree one prime ideal of norm p not dividing 6 d K . In this thesis we generalize an algorithm of Schoof to compute the class number of ray class fields [Special characters omitted.] heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura's reciprocity law. We have discovered a very interesting phenomena where p divides the class number of [Special characters omitted.] . This is a counterexample to the elliptic analogue of a well-known conjecture, namely the Vandiver's conjecture.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:open_access_dissertations-1055 |
| Date | 01 May 2009 |
| Creators | Kucuksakalli, Omer |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Open Access Dissertations |
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