Abstract
In this paper we study the classical problem of reconstructing a differential equation from a given monodromy group Г in the situation when Г is a Fuchsian group of the first kind of topological genus zero. We also give a survey of the algebrotopological theory which describes the structure of the subgroups of Г, and we give examples of the calculation of the corresponding modular equations.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 162, pp. 5–42, 1987.
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Venkov, A.B. Examples of effective solution of the Riemann-Hilbert problem on construction of a differential equation from the monodromy group in the framework of the theory of automorphic functions. J Math Sci 46, 1707–1733 (1989). https://doi.org/10.1007/BF01099345
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DOI: https://doi.org/10.1007/BF01099345