  We give a new proof of Dennis Hejhal's theorem on the nondegeneracy of the
matrix that appears in the identity relating the Bergman and Szego kernels of a
smoothly bounded finitely connected domain in the plane. Mergelyan's theorem is
at the heart of the argument. We explore connections of Hejhal's theorem to
properties of the zeroes of the Szego kernel and propose some ideas to better
understand Hejhal's original theorem.
