On infinite products of functions in compact Riemann surfaces (Q2382339)

Let \(S\) be a closed Riemann surface and \(p \in S\). The author considers sequences of holomorphic maps on \(S-p\), for which \(p\) is a singularity of bounded degree polynomial exponential type (that is, locally at \(p\) they look like \(h(z)e^{P(1/z)}\), where \(h\) has a pole at \(p\) and \(P\) is a polynomial of degree at most the genus of \(S\)) and studies the convergence of it in terms of certain series obtained from the divisors of the involved functions.