Date of Award
5-2009
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Siman Wong
Second Advisor
Farshid Hajir
Third Advisor
Tom Weston
Subject Categories
Mathematics
Abstract
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.
DOI
https://doi.org/10.7275/6c2c-fv53
Recommended Citation
Kucuksakalli, Omer, "Class Numbers of Ray Class Fields of Imaginary Quadratic Fields" (2009). Open Access Dissertations. 71.
https://doi.org/10.7275/6c2c-fv53
https://scholarworks.umass.edu/open_access_dissertations/71