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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209514 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Eremenko, A. Tarasov, V. 2025-11-24T10:06:06Z 2018 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. 1815-0659 2010 Mathematics Subject Classification: 34M03; 34M35; 57M50 arXiv: 1801.08529 https://nasplib.isofts.kiev.ua/handle/123456789/209514 https://doi.org/10.3842/SIGMA.2018.058 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. A. Eremenko was supported by NSF grant DMS-1665115. V. Tarasov was supported in part by a Simons Foundation grant 430235. We thank Andrei Gabrielov for illuminating discussions of this paper and the referees whose remarks improved the exposition. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fuchsian Equations with Three Non-Apparent Singularities Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Fuchsian Equations with Three Non-Apparent Singularities |
| spellingShingle |
Fuchsian Equations with Three Non-Apparent Singularities Eremenko, A. Tarasov, V. |
| title_short |
Fuchsian Equations with Three Non-Apparent Singularities |
| title_full |
Fuchsian Equations with Three Non-Apparent Singularities |
| title_fullStr |
Fuchsian Equations with Three Non-Apparent Singularities |
| title_full_unstemmed |
Fuchsian Equations with Three Non-Apparent Singularities |
| title_sort |
fuchsian equations with three non-apparent singularities |
| author |
Eremenko, A. Tarasov, V. |
| author_facet |
Eremenko, A. Tarasov, V. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209514 |
| citation_txt |
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. |
| work_keys_str_mv |
AT eremenkoa fuchsianequationswiththreenonapparentsingularities AT tarasovv fuchsianequationswiththreenonapparentsingularities |
| first_indexed |
2025-12-07T20:59:07Z |
| last_indexed |
2025-12-07T20:59:07Z |
| _version_ |
1850886159225323520 |