Integrable systems and modular forms of level 2

Details Integrable systems and modular forms of level 2 Integrable systems and modular forms of level 2

2006-09-07

arxiv.org/abs/math/0609210v1

Mathematics

Number Theory

PACS numbers: 02.30.Ik, 02.30.Hq, 02.10.De, 02.30.Gp

Scientific paper

A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\Gamma_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Schwarz trianle function $S(0,0,1/2; z)$.

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