Integrable systems and modular forms of level 2

Mark J Ablowitz; Sarbarsh Chakravarty; Heekyoung Hahn

Integrable systems and modular forms of level 2

Number Theory 2007-05-23 v1 Classical Analysis and ODEs

Authors: Mark J Ablowitz , Sarbarsh Chakravarty , Heekyoung Hahn

Abstract

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 $S(0,0,1/2; z)$ .

Keywords

eisenstein series modular forms siegel modular forms

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@article{arxiv.math/0609210,
  title  = {Integrable systems and modular forms of level 2},
  author = {Mark J Ablowitz and Sarbarsh Chakravarty and Heekyoung Hahn},
  journal= {arXiv preprint arXiv:math/0609210},
  year   = {2007}
}

Comments

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

Integrable systems and modular forms of level 2

Abstract

Keywords

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