In the introduction for Rick Miranda's book "algebraic curves and Riemann surfaces", it says that they will prove Riemann-Roch "in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem".
I was wondering about the original adelic proof, and how it is related to the Mittag-Leffler problem. Is there a connection between adeles and the Mittag-Leffler problem?