Triangle Groups: Automorphic Forms and Nonlinear Differential Equations
We study the relations governing the ring of quasiautomorphic forms associated with triangle groups with a single cusp, thereby extending our earlier results on Hecke groups. The Eisenstein series associated with these triangle groups are shown to satisfy Ramanujan-like identities. These identities,...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211018 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations. Sujay K. Ashok, Dileep P. Jatkar and Madhusudhan Raman. SIGMA 16 (2020), 102, 13 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We study the relations governing the ring of quasiautomorphic forms associated with triangle groups with a single cusp, thereby extending our earlier results on Hecke groups. The Eisenstein series associated with these triangle groups are shown to satisfy Ramanujan-like identities. These identities, in turn, allow us to associate a nonlinear differential equation to each triangle group. We show that they are solved by the quasiautomorphic weight-2 Eisenstein series associated with the triangle group and its orbit under the group action. We conclude by discussing the Painlevé property of these nonlinear differential equations.
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| ISSN: | 1815-0659 |