Abstract
In this paper, we solve the Riemann-Hilbert problem for the Riemann equation and for the hypergeometric equation. We describe all possible representations of the monodromy of the Riemann equation. We show that if the monodromy of the Riemann equation belongs to SL(2, ℂ), then it can be realized not only by the Riemann equation, but also by the more special Riemann-Sturm-Liouville equation. For the hypergeometric equation, we construct a criterion for its monodromy group to belong to SL(2, ℤ).
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Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 753–767.
Original Russian Text Copyright ©2005 by V. A. Poberezhnyi.
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Poberezhnyi, V.A. Special Monodromy Groups and the Riemann-Hilbert Problem for the Riemann Equation. Math Notes 77, 695–707 (2005). https://doi.org/10.1007/s11006-005-0070-7
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DOI: https://doi.org/10.1007/s11006-005-0070-7