QUANTUM CORRECTION TO THE ENTROPY OF THE (2-DIMENSIONAL BLACK-HOLE(1))

The thermodynamics of the (2 + 1)-dimensional nonrotating black hole o f Banados, Teitelboim, and Zanelli is discussed. The first quantum cor rection to the Bekenstein-Hawking entropy is evaluated within the on-s hell Euclidean formalism, making use of the related Chern-Simons repre sentation of three-dimensional gravity. Horizon and ultraviolet diverg ences in the quantum correction are dealt with by a renormalization of the Newton constant. It is argued that the quantum correction due to the gravitational field shrinks the effective radius of a hole and bec omes more and more important as the evaporation process goes on, while the area lau is not violated.