Mittag-Leffler problem on a Riemann surface
= Mittag-Leffler problem on a Riemann surface
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The Mittag-Leffler problem asks for a global <meromorphic function> with prescribed <principal parts> at a discrete collection of points. For a finite collection, those principal parts define a <Čech cocycle> for the sheaf $\mathcal O$; vanishing of its class in $\check H^1(X,\mathcal O)$ is exactly the condition that the problem has a solution.