Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole

We derive an exact expression for the partition function of the Euclidean B TZ black hole. Using this, we show that for a black hole with large horizon area, the correction to the Bekenstein-Hawking entropy is -3/2 log(area), in agreement with that for the Schwarzschild black hole obtained in the fou r-dimensional canonical gravity formalism and also in a Lorentzian computat ion of BTZ black hole entropy. We find that the correct expression for the logarithmic correction in the context of the BTZ black hole comes from the modular invariance associated with the toroidal boundary of the black hole.