On finite generation of holomorphic functions on Riemann surfaces

TL;DR

This paper provides an alternative, concise proof that the algebra of holomorphic functions with polynomial growth on Riemann surfaces of nonnegative curvature is finitely generated.

Contribution

It offers a new, shorter proof of a known result regarding the finite generation of holomorphic functions on certain Riemann surfaces.

Findings

Holomorphic functions with polynomial growth form a finitely generated algebra.

The proof applies to Riemann surfaces with nonnegative curvature.

It simplifies the understanding of the algebraic structure of these functions.

Abstract

We gave an alternative short proof on the finite generation of holomorphic functions with polynomial growth on Riemann surfaces with nonnegative curvature. The first proof was due to Li and Tam.