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| _version_ | 1862652923062779904 |
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| author | Ashok, Sujay K. Jatkar, Dileep P. Raman, Madhusudhan |
| author_facet | Ashok, Sujay K. Jatkar, Dileep P. Raman, Madhusudhan |
| citation_txt | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations. Sujay K. Ashok, Dileep P. Jatkar and Madhusudhan Raman. SIGMA 16 (2020), 102, 13 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-15T16:57:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211018 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T16:57:05Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ashok, Sujay K. Jatkar, Dileep P. Raman, Madhusudhan 2025-12-22T09:30:37Z 2020 Triangle Groups: Automorphic Forms and Nonlinear Differential Equations. Sujay K. Ashok, Dileep P. Jatkar and Madhusudhan Raman. SIGMA 16 (2020), 102, 13 pages 1815-0659 2020 Mathematics Subject Classification: 34M55; 11F12; 33E30 arXiv:2004.06035 https://nasplib.isofts.kiev.ua/handle/123456789/211018 https://doi.org/10.3842/SIGMA.2020.102 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. We thank Robert Conte for helpful correspondence and Hossein Movasati for valuable discussions. We would also like to thank the anonymous referees for their valuable comments and feedback. DPJ and MR are grateful to IMSc, Chennai, for hospitality. MR acknowledges support from the Infosys Endowment for Research into the Quantum Structure of Spacetime. DPJ acknowledges support from SERB grant CRG/2018/002835. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Triangle Groups: Automorphic Forms and Nonlinear Differential Equations Article published earlier |
| spellingShingle | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations Ashok, Sujay K. Jatkar, Dileep P. Raman, Madhusudhan |
| title | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations |
| title_full | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations |
| title_fullStr | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations |
| title_full_unstemmed | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations |
| title_short | Triangle Groups: Automorphic Forms and Nonlinear Differential Equations |
| title_sort | triangle groups: automorphic forms and nonlinear differential equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211018 |
| work_keys_str_mv | AT ashoksujayk trianglegroupsautomorphicformsandnonlineardifferentialequations AT jatkardileepp trianglegroupsautomorphicformsandnonlineardifferentialequations AT ramanmadhusudhan trianglegroupsautomorphicformsandnonlineardifferentialequations |