Accessory Parameters for Four-Punctured Spheres
We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This gives an effective method to compute the uniformizing differe...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2022 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211521 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Accessory Parameters for Four-Punctured Spheres. Gabriele Bogo. SIGMA 18 (2022), 024, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862733470083579904 |
|---|---|
| author | Bogo, Gabriele |
| author_facet | Bogo, Gabriele |
| citation_txt | Accessory Parameters for Four-Punctured Spheres. Gabriele Bogo. SIGMA 18 (2022), 024, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This gives an effective method to compute the uniformizing differential equation. As an application, we compute numerically and study the local expansion of the real-analytic function associated with a four-punctured sphere, the value of its uniformizing parameter, and make some observations on its coefficients.
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| first_indexed | 2026-04-17T15:51:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211521 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:51:08Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bogo, Gabriele 2026-01-05T12:23:57Z 2022 Accessory Parameters for Four-Punctured Spheres. Gabriele Bogo. SIGMA 18 (2022), 024, 20 pages 1815-0659 2020 Mathematics Subject Classification: 30F35; 34M03; 32G15 arXiv:2004.02971 https://nasplib.isofts.kiev.ua/handle/123456789/211521 https://doi.org/10.3842/SIGMA.2022.024 We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This gives an effective method to compute the uniformizing differential equation. As an application, we compute numerically and study the local expansion of the real-analytic function associated with a four-punctured sphere, the value of its uniformizing parameter, and make some observations on its coefficients. The paper was written while I was a graduate student at SISSA (International School for Advanced Studies) in Trieste and a visiting student of the IMPRS graduate school at the Max Planck Institute for Mathematics in Bonn. I want to thank both institutions for the excellent working conditions. I want to thank my advisers, Don Zagier and Fernando Rodriguez Villegas, for their suggestions and support, and Giordano Cotti for very useful conversations. Finally, I thank the anonymous referees, whose suggestions and remarks gave a relevant contribution to improving the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Accessory Parameters for Four-Punctured Spheres Article published earlier |
| spellingShingle | Accessory Parameters for Four-Punctured Spheres Bogo, Gabriele |
| title | Accessory Parameters for Four-Punctured Spheres |
| title_full | Accessory Parameters for Four-Punctured Spheres |
| title_fullStr | Accessory Parameters for Four-Punctured Spheres |
| title_full_unstemmed | Accessory Parameters for Four-Punctured Spheres |
| title_short | Accessory Parameters for Four-Punctured Spheres |
| title_sort | accessory parameters for four-punctured spheres |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211521 |
| work_keys_str_mv | AT bogogabriele accessoryparametersforfourpuncturedspheres |