I am recently reading some materials about Riemann Surface. When I met Riemann Roch theorem, I came up with a question as follows:
If f is a non constant meromorphic function on a surface of genus g, n is the number of poles f have, counting multipliticy. What is the minimum of n, with respect to g?
In the case g = 0, n is not less than 1 for Liouville's theorem, in the case g = 1, n is not less than 2, because integration along the basic lattice is zero, while f can not be holomorphic, so it can not just have a simple pole. But when the genus is bigger, I can not proceed.
Thank you for any possible help.