Integrable systems and modular forms of level 2
Abstract
A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup 0(2) of the modular group SL2(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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