We calculate the quantum corrections to the entropy of a very large bl
ack hole, coming from the theory of a D-dimensional, noncritical boson
ic string. We show that for D > 2, as a result of modular invariance t
he entropy is uv finite though it diverges in the ir (while for D = 2
the entropy contains both uv and ir divergences). The issue of modular
invariance in field theory, in connection with black hole entropy, is
also investigated.