  We compute the logarithmic correction to black hole entropy about
exponentially suppressed saddle points of the Quantum Entropy Function
corresponding to Z(N) orbifolds of the near horizon geometry of the extremal
black hole under study. By carefully accounting for zero mode contributions we
show that the logarithmic contributions for quarter--BPS black holes in N=4
supergravity and one--eighth BPS black holes in N=8 supergravity perfectly
match with the prediction from the microstate counting. We also find that the
logarithmic contribution for half--BPS black holes in N = 2 supergravity
depends non-trivially on the Z(N) orbifold. Our analysis draws heavily on the
results we had previously obtained for heat kernel coefficients on Z(N)
orbifolds of spheres and hyperboloids in arXiv:1311.6286 and we also propose a
generalization of the Plancherel formula to Z(N) orbifolds of hyperboloids to
an expression involving the Harish-Chandra character of SL(2,R), a result which
is of possible mathematical interest.
