Narrow Results

The reconstruction of a Riemann surface starting from the meromorphic function field K, comes from Dedekind and Weber who developed an algebraic function theory in one variable over an algebraically closed field k. Alling and Greenleaf present a counterpart to this approach starting from a real algebraic curve. From this point of view, the residues theorem is a classical result which depends strongly on the algebraically closed character of the base field. In this paper, via the complex double, we translate this fact to the case where we start from a function field in one variable over R.