Geodesic
Examples of effective solution of the Riemann-Hilbert problem on renewal of a differential equation with monodromy group in the framework of the theory of automorphic functions
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 5-42

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In this paper we study the classical problem of reconstructing a differential equation from a given monodromy group $\Gamma$ in the situation when $\Gamma$ 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 $\Gamma$, and we give examples of the calculation of the corresponding modular equations. 
@article{ZNSL_1987_162_a0,
     author = {A. B. Venkov},
     title = {Examples of effective solution of the {Riemann-Hilbert} problem on renewal of a differential equation with monodromy group in the framework of the theory of automorphic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--42},
     publisher = {mathdoc},
     volume = {162},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a0/}
}
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A. B. Venkov. Examples of effective solution of the Riemann-Hilbert problem on renewal of a differential equation with monodromy group in the framework of the theory of automorphic functions. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part III, Tome 162 (1987), pp. 5-42. http://geodesic.mathdoc.fr/item/ZNSL_1987_162_a0/