Date of Award

5-2009

Document 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.

Included in

Mathematics Commons

Share

COinS