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Class Numbers of Ray Class Fields of Imaginary Quadratic Fields

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dc.contributor.advisorSiman Wong
dc.contributor.advisorFarshid Hajir
dc.contributor.advisorTom Weston
dc.contributor.authorKucuksakalli, Omer
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.date2023-09-22 20:18:13
dc.date.accessioned2024-04-26T19:53:06Z
dc.date.available2024-04-26T19:53:06Z
dc.date.issued5/1/09
dc.description.abstractLet 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.
dc.description.degreeDoctor of Philosophy (PhD)
dc.description.departmentMathematics
dc.identifier.doihttps://doi.org/10.7275/6c2c-fv53
dc.identifier.urihttps://hdl.handle.net/20.500.14394/39160
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1055&context=open_access_dissertations&unstamped=1
dc.source.statuspublished
dc.subjectClass numbers
dc.subjectComplex multiplication
dc.subjectElliptic curves
dc.subjectQuadratic fields
dc.subjectRay class fields
dc.subjectImaginary quadratic fields
dc.subjectMathematics
dc.titleClass Numbers of Ray Class Fields of Imaginary Quadratic Fields
dc.typedissertation
digcom.contributor.authorisAuthorOfPublication|email:komer@metu.edu.tr|institution:University of Massachusetts Amherst|Kucuksakalli, Omer
digcom.identifieropen_access_dissertations/71
digcom.identifier.contextkey1033658
digcom.identifier.submissionpathopen_access_dissertations/71
dspace.entity.typePublication
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