Geodesic
On Isomorphisms of Meromorphic Function Fields
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1230-1241

Voir la notice de l'article provenant de la source Cambridge University Press

In this work we deal with algebraic properties of some fields of functions meromorphic in the complex plane with a view to determining the possible isomorphisms between two such fields. Interest in problems of this type began with a paper by Bers (2), in which it was shown that the algebraic structure of the ring of functions analytic on a plane region determines the conformai structure of the region to within conformai or anti-conformal equivalence, and this result was later extended to arbitrary non-compact Riemann surfaces by Nakai (7). 
Kelleher, James J. On Isomorphisms of Meromorphic Function Fields. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1230-1241. doi: 10.4153/CJM-1968-118-8
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