Partition functions and elliptic genera from supergravity

We develop the spacetime aspects of the computation of partition functions for string/M-theory on AdS(3) x M. Subleading corrections to the semi-classical result are included systematically, laying the groundwork for comparison with CFT partition functions via the AdS(3)/CFT2 correspondence. This leads to a better understanding of the Farey tail expansion of Dijkgraaf et. al. from the point of view of bulk physics. Besides clarifying various issues, we also extend the analysis to the N = 2 setting with higher derivative effects included.