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In this paper we review the problem of divergences in one-loop thermodynamical quantities for matter fields in thermal equilibrium on a black hole background. We discuss a number of results obtained for various thermodynamical quantities. Then we discuss the ansatz called the ``literal interpretation'' of the zeroth law of black hole mechanics and try to explain the troubles of the conical defect procedure in light of this ansatz. Finally, an analysis of the consequences implied by our ansatz on the calculation of the partition function is made. 1996 The American Physical Society.
Belgiorno et al. (Sat,) studied this question.