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In (LS), Lochak and Schneps introduced the \harmonic pa- rameter g" of the Grothendieck-Teichm uller group d GT . We closely study the behavior of g on the absolute Galois group GQ using a family of lemniscate elliptic curves. We obtain a relationship of the adelic beta function and the harmonic parameter specialized in the matrix group SL2(^ Z).

Harmonic and equianharmonic equations in the Grothendieck-Teichmüller group