Fuchsian Equations with Three Non-Apparent Singularities
| dc.contributor.author | Eremenko, Alexandre | |
| dc.contributor.author | Tarasov, Vitaly | |
| dc.contributor.department | Mathematical Sciences, School of Science | en_US |
| dc.date.accessioned | 2019-03-20T13:43:19Z | |
| dc.date.available | 2019-03-20T13:43:19Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | We 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. | en_US |
| dc.eprint.version | Author's manuscript | en_US |
| dc.identifier.citation | Eremenko, A., & Tarasov, V. (2018). Fuchsian Equations with Three Non-Apparent Singularities. Symmetry, Integrability and Geometry: Methods and Applications. https://doi.org/10.3842/SIGMA.2018.058 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1805/18646 | |
| dc.language.iso | en | en_US |
| dc.publisher | National Academy of Science of Ukraine | en_US |
| dc.relation.isversionof | 10.3842/SIGMA.2018.058 | en_US |
| dc.relation.journal | Symmetry, Integrability and Geometry: Methods and Applications | en_US |
| dc.rights | Publisher Policy | en_US |
| dc.source | ArXiv | en_US |
| dc.subject | Fuchsian equations | en_US |
| dc.subject | hypergeometric equation | en_US |
| dc.subject | difference equations | en_US |
| dc.title | Fuchsian Equations with Three Non-Apparent Singularities | en_US |
| dc.type | Article | en_US |