Triangle Groups: Automorphic Forms and Nonlinear Differential Equations
Exactly Solvable and Integrable Systems
2021-07-13 v3 High Energy Physics - Theory
Number Theory
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.
Cite
@article{arxiv.2004.06035,
title = {Triangle Groups: Automorphic Forms and Nonlinear Differential Equations},
author = {Sujay K. Ashok and Dileep P. Jatkar and Madhusudhan Raman},
journal= {arXiv preprint arXiv:2004.06035},
year = {2021}
}