  We apply the method of conical singularities to calculate the tree-level
entropy and its one-loop quantum corrections for a charged Kerr black hole. The
Euclidean geometry for the Kerr-Newman metric is considered. We show that for
an arbitrary periodization in Euclidean space there exists a conical
singularity at the horizon. Its $\delta$-function like curvatures are
calculated and are shown to behave similar to the static case. The heat kernel
expansion for a scalar field on this conical space background is derived and
the (divergent) quantum correction to the entropy is obtained. It is argued
that these divergences can be removed by renormalization of couplings in the
tree-level gravitational action in a manner similar to that for a static black
hole.
