La. Takhtajan, A SIMPLE EXAMPLE OF MODULAR-FORMS AS TAU-FUNCTIONS FOR INTEGRABLE EQUATIONS, Theoretical and mathematical physics, 93(2), 1992, pp. 1308-1317
We show how classical modular forms and functions appear as tau-functi
ons for a certain integrable reduction of the self-dual Yang-Mills equ
ations obtained by S. Chakravarty, M. Ablowitz, and P. Clarkson [6]. W
e discuss possible consequences of this novel phenomenon in integrable
systems which indicate deep connections between integrable equations,
group representations, modular forms, and moduli spaces.