THE TRACE OF THE HEAT KERNEL ON A COMPACT HYPERBOLIC 3-ORBIFOLD

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H-3/GAMMA are evaluated in the cas e in which the discrete group GAMMA contains elliptic and hyperbolic e lements. It is shown that while hyperbolic elements give only exponent ially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are bri efly discussed in the examples.