Riemann existence theorem

The Riemann existence theorem is a fundamental result of the theory of Riemann surface.

Statement

Let X be a compact Riemann surface, p₁, ..., pₛ distinct points in X, and c₁, ..., cₛ ∈ C, there is a meromorphic function f∈ M(X) with f(pᵢ) = cᵢ for each i.

References

HARBATER, DAVID (2016), RIEMANN'S EXISTENCE THEOREM, "The Legacy of Bernhard Riemann After 150 Years" (ed. by L. Ji, F. Oort, S.-T. Yau), Beijing-Boston: Higher Education Press and International Press, ISBN 978-1571463180 Remmert, Reinhold (1998), From Riemann surfaces to complex spaces, France, Paris: S´emin. Congr., 3, Soc. Math

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