Magnetic fields and factored two-spheres

A magnetic monopole is placed at the center of a ball whose surface S-2 is tiled by the symmetry group, Gamma, of a regular solid. The quantum mechani cs on the two-dimensional quotient S-2/Gamma is developed and the monopole charge is found to be quantized in an expected manner. The heat-kernel and zeta -functions are evaluated and the Casimir energy is computed. Numerical approaches to the calculation of the derivative of the Barnes zeta -functi on are presented. (C) 2001 American Institute of Physics.