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We define and compute the continuous orbifold partition function and agenerating function for all $n$-point correlation functions for the rank twofree fermion vertex operator superalgebra on a genus two Riemann surface formedby self-sewing a torus. The partition function is proportional to an infinitedimensional determinant with entries arising from torus Szego kernel and thegenerating function is proportional to a finite determinant of genus two Szegokernels. These results follow from an explicit analysis of all torus $n$-pointcorrelation functions for intertwiners of the irreducible modules of theHeisenberg vertex operator algebra. We prove that the partition and $n$-pointcorrelation functions are holomorphic on a suitable domain and describe theirmodular properties. We also describe an identity for the genus two Riemanntheta series analogous to the Jacobi triple product identity.

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras II