Eremenko, AlexandreTarasov, Vitaly2019-03-202019-03-202018Eremenko, A., & Tarasov, V. (2018). Fuchsian Equations with Three Non-Apparent Singularities. Symmetry, Integrability and Geometry: Methods and Applications. https://doi.org/10.3842/SIGMA.2018.058https://hdl.handle.net/1805/18646We show that for every second order Fuchsian linear differential equation E with n singularities of which n−3 are apparent there exists a hypergeometric equation H and a linear differential operator with polynomial coefficients which maps the space of solutions of H into the space of solutions of E. This map is surjective for generic parameters. This justifies one statement of Klein (1905). We also count the number of such equations E with prescribed singularities and exponents. We apply these results to the description of conformal metrics of curvature 1 on the punctured sphere with conic singularities, all but three of them having integer angles.enPublisher PolicyFuchsian equationshypergeometric equationdifference equationsArticle