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arXiv · 2004.06035

Triangle Groups: Automorphic Forms and Nonlinear Differential Equations

Sujay K. Ashok·Dileep P. Jatkar·Madhusudhan Raman
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Abstract

We study the relations governing the ring of quasiautomorphic forms associated to triangle groups with a single cusp, thereby extending our earlier results on Hecke groups. The Eisenstein series associated to 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 to the triangle group and its orbit under the group action. We conclude by discussing the Painlev\'e property of these nonlinear differential equations.

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Sujay K. Ashok, Dileep P. Jatkar, Madhusudhan Raman. 2020-04-13. Triangle Groups: Automorphic Forms and Nonlinear Differential Equations. https://doi.org/10.3842/sigma.2020.102

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