  By matching 1/m^2 divergences in finite-volume two-point correlation
functions of the scalar or pseudoscalar densities with those obtained in chiral
perturbation theory, we derive a relation between the Dirac operator zero-mode
eigenfunctions at fixed non-trivial topology and the low-energy constants of
QCD. We investigate the feasibility of using this relation to extract the pion
decay constant, by computing the zero-mode correlation functions on the lattice
in the quenched approximation and comparing them with the corresponding
expressions in quenched chiral perturbation theory.
