Construction of the Fuchs differential equation with \(3\times 3\) residue-matrices and three singular points using logarithmization method (Q2095810)

The famous Riemann problem is the problem to find analytic functions or a Fuchsian differential equation they satisfy with a given monodromy group around a finite number of singular points. In some previous papers (e.g., [11; 21; 22] in the references cited in the current paper) the author of the paper under review obtained the logarithmization method, which gives a closed formula for a logarithm of the product of two \(2\times 2\) matrices, and applied it to the Riemann problem for a given monodromy group of order two. In this paper, extending the logarithmization method to a logarithm of the product of two \(3\times 3\) matrices, the author discusses the Riemann problem for a given monodromy group of order three around three singular points.