Partition function of dyonic black holes in N=4 string theory

The dominant contribution to the semicanonical partition function of dyonic black holes of N = 4 string theory is computed for generic charges, generalizing recent results of Shih and Yin. The result is compared to the black hole free energy obtained from the conjectured relation to topological strings. If certain perturbative corrections are included agreement is found to subleading order. These corrections modify the conjectured relation and implement covariance with respect to electric-magnetic duality transformations