We calculate the quantum corrections to the entropy of a very large black
hole, coming from the theory of a D-dimensional, non-critical bosonic string.
We show that, for D>2, as a result of modular invariance the entropy is
ultraviolet finite, although it diverges in the infrared (while for D=2 the
entropy contains both ultraviolet and infrared divergences). The issue of
modular invariance in field theory, in connection with black-hole entropy, is
also investigated.Comment: 8 pages, latex, no figure