A computational method for the construction of Siegel sets inudcomplex hyperbolic space

摘要

This thesis presents a computational method for constructing Siegel sets for the action of Gamma = SU(n; 1;O)udon HnC, where O is the ring of integers of an imaginary quadratic field with trivial class group. Theudthesis first presents a basic algorithm for computing Siegel sets and then considers practical improvementsudwhich can be made to this algorithm in order to decrease computation time. This improved algorithmudis implemented in a C++ program called siegel, the source code for which is freely available atudhttp://code.google.com/p/siegel/, and this program is used to compute explicit Siegel sets for theudaction of all applicable groups Gamma on H2C and H3C.