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The one-dimensional Riemann problem on an elliptic curve

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A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of… Click to show full abstract

A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.

Keywords: dimensional riemann; problem; one dimensional; elliptic curve; riemann

Journal Title: Mathematical Notes
Year Published: 2017

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