A computational method for the construction of Siegel sets in complex hyperbolic space

This thesis presents a computational method for constructing Siegel sets for the action of Γ = SU(n,1;O) on HC, where O is the ring of integers of an imaginary quadratic field with trivial class group. The thesis first presents a basic algorithm for computing Siegel sets and then considers practical improvements which can be made to this algorithm in order to decrease computation time. This improved algorithm is implemented in a C++ program called siegel, the source code for which is freely available at http://code.google.com/p/siegel/, and this program is used to compute explicit Siegel sets for the action of all applicable groups Γ on HC and HC.