Fuchsian Equations with Three Non-Apparent Singularities
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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209514 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Fuchsian Equations with Three Non-Apparent Singularities / A. Eremenko, V. Tarasov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1815-0659 |