Partition Functions of Three-Dimensional Quantum Gravity and the Black   Hole Entropy
  We analyze aspects of the holographic principle relevant to the quantum gravity partition functions in Euclidean sector of AdS$_3$. The sum of the known contributions to the partitions functions can be presented exactly, including corrections, in the form where the Patterson-Selberg zeta function involves. 
A. A. Bytsenko (DF/Uel) and M. E. X. Guimaraes (IF/Uff)