I am looking for a reference which explains how theta functions, algebraically independent meromorphic functions, and line bundles all fit together in the context of complex tori. More explicitly, given the right kind of Hermitian form on $\mathbb{C}^g$ with respect to some lattice $L$ I'd like an explicit construction of the g independent meromorphic functions on $\mathbb{C}^g/L$, which is something that Mumford, for example, does not give.