The Ramond-Ramond self-dual Five-form's Partition Function on the Ten Torus

In view of the recent interest in formulating a quantum theory of Ramond-Ramond p-forms, we exhibit an SL(10,Z) invariant partition function for the chiral four-form of Type IIB string theory on the ten-torus. We follow the strategy used to derive a modular invariant partition function for the chiral two-form of the M-theory fivebrane. We also generalize the calculation to self-dual quantum fields in spacetime dimension 2p=2+4k, and display the SL(2p,Z) automorphic forms for odd p>1. We relate our explicit calculation to a computation of the B-cycle periods, which are discussed in the work of Witten.