Date of Award
5-2009
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Wong, Siman
Second Advisor
Hajir, Farshid
Third Advisor
Weston, Tom
Keywords
Class numbers, Complex multiplication, Elliptic curves, Quadratic fields, Ray class fields, Imaginary quadratic fields
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.
Recommended Citation
Kucuksakalli, Omer, "Class Numbers of Ray Class Fields of Imaginary Quadratic Fields" (2009). Open Access Dissertations. Paper 71.
http://scholarworks.umass.edu/open_access_dissertations/71