Nevanlinna theory via holomorphic forms

. This paper re-develops Nevanlinna theory for meromorphic functions on C in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form. Applying this thought to Riemann surfaces, one then extends the definition of Nevanlinna’s functions using a holomorphic form S . With the new settings, an analogue of Nevanlinna theory on the S -exhausted Riemann surfaces is obtained, which is viewed as a generalization of the classical Nevanlinna theory for C and D .