| Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known.;In the final chapter we consider the case lambda = -1 from a numerical point of view and develop an efficient algorithm to compute S-1 without computing class numbers.;Hooley [5] derived a conjectural formula for the average of class numbers of real quadratic fields, Sx= D≤xhD. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, Slx= D≤xhD l, where lambda is an arbitrary real number. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work. |
