Class numbers of ray class fields of
imaginary quadratic fields
(University of Massachusetts)
Abstract: The class number is a powerful invariant in
algebraic number theory which can be used to investigate the integer solutions
of polynomials, such as Fermat's Equation. It can be computed for extensions
with small degree and
discriminant, however computations take a very long time for higher extensions. In this talk, we will describe a heuristic method to compute the class numbers of ray class fields of imaginary quadratic fields, the elliptic curve analogue of real cyclotomic fields. We will use elliptic units analytically constructed by Stark and the Galois action on them given by Shimura's reciprocity. In the end we will give a counter example to Vandiver's conjecture in the elliptic curve case.In my talk I am going to present the new trends in the area of fractional calculus. Several recent applications of this type of calculus in economics, bioengineering, physics and engineering will be illustrated.
Date : December 18, 2008 (Thursday)
Time : 15.40
Place: Mathematics Seminar Room SA141
Tea will be served before the seminar.