VACUUM ENERGY ON ORBIFOLD FACTORS OF SPHERES

The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time R x S2/GAMMA where GAMMS is a finite subgroup of O(3) acting with fixed points. The energy vanishes when G AMMA is composed of pure rotations but not otherwise. It is shown on g eneral grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Ber noulli functions. The relevant zeta-functions are analysed in some det ail and several identities are incidentally derived. The general discu ssion is presented in terms of finite reflection groups.