Integrable systems and modular forms of level 2

2006/09/07 by Mark J Ablowitz, Ablowitz, Mark J, Sarbarsh Chakravarty +3
Mathematics · #11F03 #11F11 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:11F03 #msc:11F11

paper · pdf · doi:10.48550/arxiv.math/0609210

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

arxiv created 2006/09/07 · arxiv updated 2009/12/01

Abstract

A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup Γ₀(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).

Related

• On level 2 Modular differential equations
• Defining differential equations for modular forms and Jacobi forms
• Differential equations satisfied by modular forms of level 5
• Differential equations involving cubic theta functions and Eisenstein series
• Equivariant solutions to modular Schwarzian equations