On directional derivatives of the theta function along its divisor (Q1802721)

In this paper the author extends a theorem of Farkas by identifying the zero set of any directional derivative of the theta function evaluated at any point in the theta divisor with the divisor of a determinant formed from a \(g-1\) dimensional subspace of holomorphic one-forms from the underlying Riemann surface. He also presents a review of the problem of analytic torsion for degree zero line bundles on Riemann surfaces.