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The number of additional singular points in the Riemann-Hilbert problem on a Riemann surface

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Abstract

We present an upper bound for the number of additional singular points that are sufficient to construct a system of linear equations with given regular singular points and a given monodromy on a Riemann surface.

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References

  1. A. A. Bolibrukh, Inverse Monodromy Problems in the Analytic Theory of Differential Equations (MTsNMO, Moscow, 2009) [in Russian].

    Google Scholar 

  2. M. Ohtsuki, “On the number of apparent singularities of a linear differential equation,” Tokyo J. Math. 5(1), 23–29 (1982).

    Article  MathSciNet  Google Scholar 

  3. A. A. Bolibrukh, “The Riemann-Hilbert problem on a compact Riemann surface,” in Monodromy in Problems of Algebraic Geometry and Differential Equations, Collected papers (Nauka, Moscow, 2002), Vol. 238, pp. 55–69 [Proc. Steklov Inst.Math. 238 (3), 47–60 (2002)].

    Google Scholar 

  4. M. Yoshida, “On the number of apparent singularities of the Riemann-Hilbert problem on Riemann surface,” J. Math. Soc. Japan 49(1), 145–159 (1997).

    Article  MathSciNet  Google Scholar 

  5. O. Forster, Lectures on Riemann Surfaces(Springer, Berlin, 1977 [in German]; Springer-Verlag, New York, 1991)

    Google Scholar 

  6. I. M. Krichever and S. P. Novikov, “Holomorphic vector bundles over Riemann surfaces and the Kadomtsev-Petviashvili equation. I,” Funktsional. Anal. Prilozhen. 12(4), 41–52 (1978) [Functional Anal. Appl. 12 (4), 276–286 (1978) (1979)].

    MathSciNet  Google Scholar 

  7. A. N. Tyurin [Tjurin], “The classification of vector bundles over an algebraic curve of arbitrary genus,” Izv. Akad. Nauk SSSR Ser. Mat. 29(3), 657–688 (1965) [Amer. Math. Soc. Translat., II 63, 245–279 (1967)].

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    D. V. Artamonov

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  1. D. V. Artamonov
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Correspondence to D. V. Artamonov.

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Original Russian Text © D. V. Artamonov, 2011, published in Matematicheskie Zametki, 2011, Vol. 90, No. 1, pp. 3–10.

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Artamonov, D.V. The number of additional singular points in the Riemann-Hilbert problem on a Riemann surface. Math Notes 90, 3 (2011). https://doi.org/10.1134/S0001434611070017

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  • DOI: https://doi.org/10.1134/S0001434611070017

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