The Serre duality theorem for Riemann surfaces (Q760541)

Let S be a compact Riemann surface of genus \(g\geq 2\), and suppose that G is the associated Fuchsian group acting on the upper half plane U. In this paper the author gives a proof of the Serre duality theorem which avoids sheaf theoretical methods. The method of proof is to use Fuchsian group methods. As noted by the author the main ideas for the proof are contained in the text of \textit{I. Kra} (Automorphic forms and Kleinian groups (1972; Zbl 0253.30015).