Adelic Eisenstein function on elliptic Grothendieck-Teichmueller group

I will introduce an elliptic variant of Anderson-Ihara beta function, called adelic Eisenstein function on the Galois-fundamental group of the moduli space of elliptic curves. In particular, I will illustrate how it extends to a function on the elliptic Grothendieck-Teichmueller group introduced by B.Enriquez.