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Class numbers of ray class fields of imaginary quadratic fields
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 6dK. 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.
Subject Area
Mathematics
Recommended Citation
Kucuksakalli, Omer, "Class numbers of ray class fields of imaginary quadratic fields" (2009). Doctoral Dissertations Available from Proquest. AAI3359147.
https://scholarworks.umass.edu/dissertations/AAI3359147