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Construction of the Fuchs Differential Equation with \(\mathbf{3\times 3}\) Residue-Matrices and Three Singular Points Using Logarithmization Method

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Abstract

A solution of the problem of Riemann is constructed for a system of three analytic functions with a given monodromy group and three singular points. The canonical matrix of the problem was constructed. A new method for constructing residue-matrices for the Riemann problem with third-order monodromy group is proposed. We obtained a closed formula for a logarithm of a product of two matrices for the third-order monodromy group. Using the logarithmization method we have constructed \(3\times 3\) residue-matrices for the Fuchs equation with three singular points.

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Authors and Affiliations

  1. International Sakharov Environmental Institute of Belarusian State University, 220037, Minsk, Belarus

    L. A. Khvoshchinskaya

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  1. L. A. Khvoshchinskaya
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Correspondence to L. A. Khvoshchinskaya.

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(Submitted by A. B. Muravnik)

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Khvoshchinskaya, L.A. Construction of the Fuchs Differential Equation with \(\mathbf{3\times 3}\) Residue-Matrices and Three Singular Points Using Logarithmization Method. Lobachevskii J Math 43, 1337–1344 (2022). https://doi.org/10.1134/S199508022209013X

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  • DOI: https://doi.org/10.1134/S199508022209013X

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