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 Mat. Zametki, 2005, Volume 77, Issue 5, Pages 753–767 (Mi mz2532)

Special Monodromy Groups and the Riemann–Hilbert Problem for the Riemann Equation

V. A. Poberezhnyi

Steklov Mathematical Institute, Russian Academy of Sciences

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 $SL(2,\mathbb C)$, 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 $SL(2,\mathbb Z)$.

DOI: https://doi.org/10.4213/mzm2532

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English version:
Mathematical Notes, 2005, 77:5, 695–707

Bibliographic databases:

UDC: 517.9+524.745.87

Citation: V. A. Poberezhnyi, “Special Monodromy Groups and the Riemann–Hilbert Problem for the Riemann Equation”, Mat. Zametki, 77:5 (2005), 753–767; Math. Notes, 77:5 (2005), 695–707

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz2532
• https://doi.org/10.4213/mzm2532
• http://mi.mathnet.ru/eng/mz/v77/i5/p753

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. D. V. Anosov, “On the Projects “Inverse Monodromy Problems and Isomonodromic Deformations,” “Wave Processes in Media with Diffusion,” and “Nonlinear Dynamics of Low-Dimensional Systems with Irregular Behavior of Trajectories””, Proc. Steklov Inst. Math., 251 (2005), 3–5
2. R. R. Gontsov, V. A. Poberezhnyi, “Various versions of the Riemann–Hilbert problem for linear differential equations”, Russian Math. Surveys, 63:4 (2008), 603–639
3. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33
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